diff --git a/src/core/commands/assetCommands.ts b/src/core/commands/assetCommands.ts
index 6cd66e3e..070abdfa 100644
--- a/src/core/commands/assetCommands.ts
+++ b/src/core/commands/assetCommands.ts
@@ -6,12 +6,13 @@ import { isFontFile } from '../model/font';
 import { removeSubtrees } from '../model/hierarchy';
 import type { PropertyBag, PropertyValue } from '../model/Properties';
 import { objectHolders, type Project } from '../model/Project';
+import { type Scope, scopeOf, setScope } from '../model/Scope';
 import type { SceneObject } from '../model/SceneObject';
 import { isTextureFile } from '../model/texture';
 import { coerceValue, defaultsFor } from '../properties/PropertySchema';
 import { type Removed, removeById, removeFirst, restoreAt } from '../util/list';
 import { type Command, CommandError } from './Command';
-import { requireAsset, requirePropDef } from './require';
+import { requireAsset, requirePropDef, requireStateMachine } from './require';
 import { SetBagValueCommand } from './SetBagValueCommand';
 
 export function buildAsset(type: AssetType, name: string, id = newId()): Asset {
@@ -215,6 +216,29 @@ export class RenameAssetCommand implements Command {
   }
 }
 
+/** A `global` machine keeps one current state for the whole run instead of one per behavior instance. */
+export class SetMachineScopeCommand implements Command {
+  readonly label: string;
+  private previous: Scope = 'local';
+
+  constructor(
+    private readonly assetId: string,
+    private readonly scope: Scope,
+  ) {
+    this.label = `Make state machine ${scope}`;
+  }
+
+  execute(project: Project): void {
+    const asset = requireStateMachine(project, this.assetId);
+    this.previous = scopeOf(asset);
+    setScope(asset, this.scope);
+  }
+
+  undo(project: Project): void {
+    setScope(requireStateMachine(project, this.assetId), this.previous);
+  }
+}
+
 abstract class AssetPropertyCommand extends SetBagValueCommand<Asset> {
   protected constructor(
     private readonly assetId: string,
diff --git a/src/core/commands/require.ts b/src/core/commands/require.ts
index d249dcc0..1ef0d2ee 100644
--- a/src/core/commands/require.ts
+++ b/src/core/commands/require.ts
@@ -1,7 +1,7 @@
 /** Lookups that throw a `CommandError` when the target does not exist. */
 import { findNode, type Graph, type GraphNode } from '../graph/Graph';
 import { type NodeDef, nodeDef } from '../graph/NodeRegistry';
-import type { Asset, BehaviorAsset } from '../model/Asset';
+import type { Asset, BehaviorAsset, StateMachineAsset } from '../model/Asset';
 import { findObject, type ObjectTree } from '../model/hierarchy';
 import { isTemplateContent, objectRef, type ObjectRef } from '../model/instance';
 import {
@@ -71,6 +71,12 @@ export function requireBehavior(project: Project, assetId: string): BehaviorAsse
   return asset;
 }
 
+export function requireStateMachine(project: Project, assetId: string): StateMachineAsset {
+  const asset = findAssetOf(project, assetId, 'statemachine');
+  if (!asset) throw new CommandError(`State machine ${assetId} not found`);
+  return asset;
+}
+
 /** The graph of a behavior or of a state machine – what every graph command edits. */
 export function requireGraph(project: Project, assetId: string): Graph {
   const asset = findGraphAsset(project, assetId);
diff --git a/src/core/commands/variableCommands.ts b/src/core/commands/variableCommands.ts
index 40773569..1f631071 100644
--- a/src/core/commands/variableCommands.ts
+++ b/src/core/commands/variableCommands.ts
@@ -7,6 +7,7 @@ import {
 } from '../model/Properties';
 import { overrideSites } from '../model/instance';
 import type { Project } from '../model/Project';
+import { type Scope, scopeOf, setScope } from '../model/Scope';
 import type { VariableKind } from '../properties/kinds';
 import {
   emptyFieldValue,
@@ -51,11 +52,45 @@ export class AddVariableCommand implements Command {
   }
 }
 
+/** One placed object's own value for a variable, remembered so that undo can put it back. */
+interface TakenOverride {
+  holderId: string;
+  objectId: string;
+  path: string;
+  value: PropertyValue;
+}
+
+function takeOverrides(project: Project, assetId: string, key: string): TakenOverride[] {
+  const taken: TakenOverride[] = [];
+  for (const site of overrideSites(project, (id) => id === assetId)) {
+    const value = site.bag[key];
+    if (value === undefined) continue;
+    taken.push({ holderId: site.holder.id, objectId: site.object.id, path: site.path, value });
+    delete site.bag[key];
+  }
+  return taken;
+}
+
+function restoreOverrides(
+  project: Project,
+  assetId: string,
+  key: string,
+  taken: readonly TakenOverride[],
+): void {
+  const sites = overrideSites(project, (id) => id === assetId);
+  for (const o of taken) {
+    const site = sites.find(
+      (s) => s.holder.id === o.holderId && s.object.id === o.objectId && s.path === o.path,
+    );
+    if (site) site.bag[key] = o.value;
+  }
+}
+
 /** Removes a variable together with its default and every instance override. */
 export class RemoveVariableCommand implements Command {
   readonly label: string;
   private removed?: { def: Removed<PropertyDef>; value: PropertyValue | undefined };
-  private overrides: { holderId: string; objectId: string; path: string; value: PropertyValue }[] = [];
+  private overrides: TakenOverride[] = [];
 
   constructor(
     private readonly assetId: string,
@@ -70,13 +105,7 @@ export class RemoveVariableCommand implements Command {
     if (!def) throw new CommandError(`Variable "${this.key}" not found`);
     this.removed = { def, value: asset.props[this.key] };
     delete asset.props[this.key];
-    this.overrides = [];
-    for (const site of overrideSites(project, (id) => id === this.assetId)) {
-      const value = site.bag[this.key];
-      if (value === undefined) continue;
-      this.overrides.push({ holderId: site.holder.id, objectId: site.object.id, path: site.path, value });
-      delete site.bag[this.key];
-    }
+    this.overrides = takeOverrides(project, this.assetId, this.key);
   }
 
   undo(project: Project): void {
@@ -84,13 +113,40 @@ export class RemoveVariableCommand implements Command {
     const asset = requireBehavior(project, this.assetId);
     restoreAt(asset.variables, [this.removed.def]);
     if (this.removed.value !== undefined) asset.props[this.key] = this.removed.value;
-    const sites = overrideSites(project, (id) => id === this.assetId);
-    for (const o of this.overrides) {
-      const site = sites.find(
-        (s) => s.holder.id === o.holderId && s.object.id === o.objectId && s.path === o.path,
-      );
-      if (site) site.bag[this.key] = o.value;
-    }
+    restoreOverrides(project, this.assetId, this.key, this.overrides);
+  }
+}
+
+/**
+ * A shared variable has no per-instance value, so going `global` takes the deviations placed objects
+ * kept for it. Undo gives them back.
+ */
+export class SetVariableScopeCommand implements Command {
+  readonly label: string;
+  private previous: Scope = 'local';
+  private overrides: TakenOverride[] = [];
+
+  constructor(
+    private readonly assetId: string,
+    private readonly key: string,
+    private readonly scope: Scope,
+  ) {
+    this.label = `Make variable ${key} ${scope}`;
+  }
+
+  execute(project: Project): void {
+    const def = variableOf(project, this.assetId, this.key);
+    if (!def) throw new CommandError(`Variable "${this.key}" not found`);
+    this.previous = scopeOf(def);
+    setScope(def, this.scope);
+    this.overrides = this.scope === 'global' ? takeOverrides(project, this.assetId, this.key) : [];
+  }
+
+  undo(project: Project): void {
+    const def = variableOf(project, this.assetId, this.key);
+    if (!def) return;
+    setScope(def, this.previous);
+    restoreOverrides(project, this.assetId, this.key, this.overrides);
   }
 }
 
diff --git a/src/core/graph/NodeContext.ts b/src/core/graph/NodeContext.ts
index 89d5e3b1..ee03c8cb 100644
--- a/src/core/graph/NodeContext.ts
+++ b/src/core/graph/NodeContext.ts
@@ -69,6 +69,16 @@ export interface PointerState {
   released: boolean;
 }
 
+/**
+ * What `global` declarations share for the length of one run: one value per variable name, one
+ * current state per machine. A key that is not in here is not shared – which is what lets a behavior
+ * declaring the same name for itself keep its own value (see `graph/sharedState.ts`).
+ */
+export interface SharedState {
+  variables: PropertyBag;
+  states: Record<string, string>;
+}
+
 /**
  * Everything the graph does to the world goes through here, so the core stays free of runtime
  * imports. Implemented by the runtime (BehaviorSystem) and by test doubles.
@@ -83,6 +93,7 @@ export interface NodeContext {
    * as the state node's id. A machine not in here is in no state: `State branch` follows nothing.
    */
   states: Record<string, string>;
+  shared: SharedState;
   /** Seconds since the world started and since the last tick. */
   time: number;
   dt: number;
diff --git a/src/core/graph/index.ts b/src/core/graph/index.ts
index b0e5263b..a55f5c9b 100644
--- a/src/core/graph/index.ts
+++ b/src/core/graph/index.ts
@@ -8,6 +8,7 @@ export * from './nested';
 export * from './NodeContext';
 export * from './NodeRegistry';
 export * from './propertyPorts';
+export * from './sharedState';
 export * from './stateMachine';
 export * from './values';
 export * from './variablePorts';
diff --git a/src/core/graph/nodes/flow/SetState.ts b/src/core/graph/nodes/flow/SetState.ts
index e4d77866..62ba7de1 100644
--- a/src/core/graph/nodes/flow/SetState.ts
+++ b/src/core/graph/nodes/flow/SetState.ts
@@ -1,4 +1,5 @@
 import type { NodeDef } from '../../NodeRegistry';
+import { stateBag } from '../../sharedState';
 import { machineOf, machinePort, statePorts } from '../../stateMachine';
 import { asString } from '../../values';
 import { exec } from '../shared';
@@ -10,14 +11,15 @@ export const SetState: NodeDef = {
   category: 'action',
   description:
     'Puts the machine into the state whose input the flow arrived through, then continues. Each ' +
-    'behavior instance keeps its own states.',
+    'behavior instance keeps its own states, unless the machine is global.',
   inputs: [machinePort()],
   outputs: [exec()],
   params: [],
   derivePorts: (source) => ({ inputs: statePorts(machineOf(source)) }),
   run: (ctx, inputs, _params, def, entry) => {
     const machine = asString(inputs.machine);
-    if (machine && def.inputs.some((p) => p.type === 'exec' && p.key === entry)) ctx.states[machine] = entry;
+    if (machine && def.inputs.some((p) => p.type === 'exec' && p.key === entry))
+      stateBag(ctx, machine)[machine] = entry;
     return { next: 'exec' };
   },
 };
diff --git a/src/core/graph/nodes/flow/StateBranch.ts b/src/core/graph/nodes/flow/StateBranch.ts
index 46eba4a2..449576b0 100644
--- a/src/core/graph/nodes/flow/StateBranch.ts
+++ b/src/core/graph/nodes/flow/StateBranch.ts
@@ -1,4 +1,5 @@
 import type { NodeDef } from '../../NodeRegistry';
+import { stateBag } from '../../sharedState';
 import { machineOf, machinePort, statePorts } from '../../stateMachine';
 import { asString } from '../../values';
 import { exec } from '../shared';
@@ -16,7 +17,8 @@ export const StateBranch: NodeDef = {
   params: [],
   derivePorts: (source) => ({ outputs: statePorts(machineOf(source)) }),
   run: (ctx, inputs, _params, def) => {
-    const current = ctx.states[asString(inputs.machine)];
+    const machine = asString(inputs.machine);
+    const current = stateBag(ctx, machine)[machine];
     return def.outputs.some((p) => p.key === current) ? { next: current } : {};
   },
 };
diff --git a/src/core/graph/nodes/flow/StateTransition.ts b/src/core/graph/nodes/flow/StateTransition.ts
index 1095b5ae..7e819962 100644
--- a/src/core/graph/nodes/flow/StateTransition.ts
+++ b/src/core/graph/nodes/flow/StateTransition.ts
@@ -1,6 +1,7 @@
 import { textOf } from '../../../model/Properties';
 import { flatDef } from '../../../properties/PropertySchema';
 import type { NodeDef } from '../../NodeRegistry';
+import { stateBag } from '../../sharedState';
 import { machinePort, STATE_TRANSITION, TRANSITION_PARAM, transitionTo } from '../../stateMachine';
 import { asString } from '../../values';
 import { exec } from '../shared';
@@ -18,11 +19,12 @@ export const StateTransition: NodeDef = {
   params: [flatDef(TRANSITION_PARAM, 'text', { label: 'Transition', value: '' })],
   run: (ctx, inputs, params, _def, _entry, lookup) => {
     const id = asString(inputs.machine);
-    const current = ctx.states[id] ?? '';
+    const states = stateBag(ctx, id);
+    const current = states[id] ?? '';
     const machine = current ? lookup.machine(id) : null;
     const name = textOf(params[TRANSITION_PARAM] ?? '');
     const target = machine ? transitionTo(machine, current, name) : '';
-    if (target) ctx.states[id] = target;
+    if (target) states[id] = target;
     return { next: 'exec' };
   },
 };
diff --git a/src/core/graph/nodes/variable/Variables.ts b/src/core/graph/nodes/variable/Variables.ts
index c8dc5164..b523d48b 100644
--- a/src/core/graph/nodes/variable/Variables.ts
+++ b/src/core/graph/nodes/variable/Variables.ts
@@ -1,5 +1,6 @@
 import { collapsedTitle, portDefOf, VARIABLES } from '../../nested';
 import { type NodeDef, withInlineDefault } from '../../NodeRegistry';
+import { readableVariables, variableBag } from '../../sharedState';
 import { writeTyped } from '../../values';
 import { exec } from '../shared';
 
@@ -24,10 +25,10 @@ export const Variables: NodeDef = {
     const shape = ports.some((p) => p.write) ? { inputs: [exec()], outputs: [exec()] } : {};
     return node.collapsed ? { ...shape, label: collapsedTitle(ports, 'variables') } : shape;
   },
-  read: (ctx) => ctx.variables,
+  read: (ctx) => readableVariables(ctx),
   run: (ctx, inputs, _params, def) => {
     for (const port of def.inputs)
-      if (port.type !== 'exec') writeTyped(ctx.variables, port.key, inputs[port.key]);
+      if (port.type !== 'exec') writeTyped(variableBag(ctx, port.key), port.key, inputs[port.key]);
     return { next: 'exec' };
   },
 };
diff --git a/src/core/graph/sharedState.ts b/src/core/graph/sharedState.ts
new file mode 100644
index 00000000..133ff07b
--- /dev/null
+++ b/src/core/graph/sharedState.ts
@@ -0,0 +1,115 @@
+import type { Asset } from '../model/Asset';
+import type { PropertyBag, PropertyValue } from '../model/Properties';
+import type { Project } from '../model/Project';
+import { isGlobal } from '../model/Scope';
+import type { PropertyDef } from '../properties/PropertySchema';
+import type { NodeContext, SharedState } from './NodeContext';
+
+export function emptySharedState(): SharedState {
+  return { variables: {}, states: {} };
+}
+
+/**
+ * Built once per run, from the declarations rather than from any instance: a global variable exists
+ * even before the behavior declaring it is placed. Two behaviors declaring the same name mean the
+ * same variable – the first declaration sets the starting value (see `globalConflicts`).
+ */
+export function buildSharedState(project: Project): SharedState {
+  const shared = emptySharedState();
+  for (const asset of project.assets) {
+    if (asset.type === 'behavior') {
+      for (const def of asset.variables)
+        if (isGlobal(def) && !(def.key in shared.variables))
+          shared.variables[def.key] = asset.props[def.key] ?? def.default;
+    } else if (asset.type === 'statemachine' && isGlobal(asset)) {
+      shared.states[asset.id] = '';
+    }
+  }
+  return shared;
+}
+
+/**
+ * Where two behaviors disagree about the same global name. A different kind is an error – one of the
+ * two would silently read a value of a type it never declared – while a different starting value is
+ * only a warning, since the first declaration decides and the run is well defined either way.
+ */
+export interface GlobalConflict {
+  key: string;
+  severity: 'error' | 'warning';
+  message: string;
+}
+
+export function globalConflicts(project: Project): GlobalConflict[] {
+  const first = new Map<string, { def: PropertyDef; asset: string; value: PropertyValue }>();
+  const conflicts: GlobalConflict[] = [];
+  const seen = new Set<string>();
+  for (const asset of project.assets) {
+    if (asset.type !== 'behavior') continue;
+    for (const def of asset.variables) {
+      if (!isGlobal(def)) continue;
+      const value = asset.props[def.key] ?? def.default;
+      const held = first.get(def.key);
+      if (!held) {
+        first.set(def.key, { def, asset: asset.name, value });
+        continue;
+      }
+      // One report per name: a third behavior disagreeing adds nothing the first line does not say.
+      if (seen.has(def.key)) continue;
+      if (held.def.kind !== def.kind) {
+        seen.add(def.key);
+        conflicts.push({
+          key: def.key,
+          severity: 'error',
+          message: `Global variable "${def.key}" is a ${held.def.kind} in ${held.asset} and a ${def.kind} in ${asset.name}.`,
+        });
+      } else if (!sameValue(held.value, value)) {
+        seen.add(def.key);
+        conflicts.push({
+          key: def.key,
+          severity: 'warning',
+          message: `Global variable "${def.key}" starts at ${display(held.value)} in ${held.asset} and at ${display(value)} in ${asset.name}; the first is used.`,
+        });
+      }
+    }
+  }
+  return conflicts;
+}
+
+/** Structs and lists compare by their stored shape, which is what the project file holds anyway. */
+function sameValue(a: PropertyValue | undefined, b: PropertyValue | undefined): boolean {
+  return a === b || JSON.stringify(a ?? null) === JSON.stringify(b ?? null);
+}
+
+function display(value: PropertyValue | undefined): string {
+  return typeof value === 'string' ? `"${value}"` : JSON.stringify(value ?? null);
+}
+
+/** The bag a variable is written to: its own when the behavior declares it, else the shared one. */
+export function variableBag(ctx: NodeContext, key: string): PropertyBag {
+  if (key in ctx.variables) return ctx.variables;
+  return key in ctx.shared.variables ? ctx.shared.variables : ctx.variables;
+}
+
+/** Everything the behavior can read under one name, its own declaration winning over a shared one. */
+export function readableVariables(ctx: NodeContext): PropertyBag {
+  const shared = ctx.shared.variables;
+  return isEmpty(shared) ? ctx.variables : { ...shared, ...ctx.variables };
+}
+
+/** Where a machine's current state is kept: shared when the machine is `global`, else per instance. */
+export function stateBag(ctx: NodeContext, machineId: string): Record<string, string> {
+  return machineId in ctx.shared.states ? ctx.shared.states : ctx.states;
+}
+
+/** The defaults a behavior instance starts with: a shared variable is not one of them. */
+export function withoutGlobals(defaults: PropertyBag, asset: Asset): PropertyBag {
+  if (asset.type !== 'behavior') return defaults;
+  const own = { ...defaults };
+  for (const def of asset.variables) if (isGlobal(def)) delete own[def.key];
+  return own;
+}
+
+function isEmpty(bag: PropertyBag): boolean {
+  for (const key in bag) if (Object.hasOwn(bag, key)) return false;
+  return true;
+}
diff --git a/src/core/model/Asset.ts b/src/core/model/Asset.ts
index 4c1713c8..6b654a4e 100644
--- a/src/core/model/Asset.ts
+++ b/src/core/model/Asset.ts
@@ -2,6 +2,7 @@ import type { Graph } from '../graph/Graph';
 import type { PropertyDef } from '../properties/PropertySchema';
 import type { AssetType } from './AssetTypes';
 import type { PropertyBag } from './Properties';
+import type { Scope } from './Scope';
 import type { SceneObject } from './SceneObject';
 
 export interface AssetBase {
@@ -85,10 +86,12 @@ export interface AnimationAsset extends AssetBase {
 /**
  * The graph holds one `State` node per state and an edge per transition; a behavior reads the
  * machine's current state through `State branch` and moves it through `Set state` or `State transition`.
+ * A `global` machine has one current state for the whole run instead of one per behavior instance.
  */
 export interface StateMachineAsset extends AssetBase {
   type: 'statemachine';
   graph: Graph;
+  scope?: Scope;
 }
 
 /**
diff --git a/src/core/model/Scope.ts b/src/core/model/Scope.ts
new file mode 100644
index 00000000..9012e9ff
--- /dev/null
+++ b/src/core/model/Scope.ts
@@ -0,0 +1,29 @@
+/**
+ * Whether a declaration keeps a value per behavior instance or shares one for the whole run.
+ * Everything was `local` before scopes existed, so a missing field means `local` and old projects
+ * load unchanged.
+ */
+export type Scope = 'local' | 'global';
+
+export interface Scoped {
+  scope?: Scope;
+}
+
+export function scopeOf(owner: Scoped): Scope {
+  return owner.scope === 'global' ? 'global' : 'local';
+}
+
+export function isGlobal(owner: Scoped): boolean {
+  return owner.scope === 'global';
+}
+
+/** Reads a scope out of loaded data, where anything but the one known word means `local`. */
+export function readScope(raw: unknown): Scope {
+  return raw === 'global' ? 'global' : 'local';
+}
+
+/** Keeps `local` out of the document: the field is present only when it says `global`. */
+export function setScope(owner: Scoped, scope: Scope): void {
+  if (scope === 'global') owner.scope = 'global';
+  else delete owner.scope;
+}
diff --git a/src/core/model/graphLookup.ts b/src/core/model/graphLookup.ts
index 6ba0592c..ec57b000 100644
--- a/src/core/model/graphLookup.ts
+++ b/src/core/model/graphLookup.ts
@@ -1,4 +1,5 @@
 import type { GraphLookup } from '../graph/lookup';
+import { withoutGlobals } from '../graph/sharedState';
 import { statesOf, transitionsOf } from '../graph/stateMachine';
 import { resolveAssetProps } from '../properties/resolve';
 import { findAssetOf, type Project } from './Project';
@@ -12,7 +13,8 @@ export function graphLookup(project: Project): GraphLookup {
     behavior: (assetId) => {
       const asset = findAssetOf(project, assetId, 'behavior');
       if (!asset) return null;
-      return { name: asset.name, graph: asset.graph, defaults: resolveAssetProps(project, asset) };
+      const defaults = withoutGlobals(resolveAssetProps(project, asset), asset);
+      return { name: asset.name, graph: asset.graph, defaults };
     },
     machine: (assetId) => {
       const asset = findAssetOf(project, assetId, 'statemachine');
diff --git a/src/core/properties/PropertySchema.ts b/src/core/properties/PropertySchema.ts
index a9dc3b15..e67b46e2 100644
--- a/src/core/properties/PropertySchema.ts
+++ b/src/core/properties/PropertySchema.ts
@@ -20,6 +20,7 @@ import {
   type VariableKind,
 } from './kinds';
 import { findAssetOf, type Project } from '../model/Project';
+import { isGlobal, type Scope } from '../model/Scope';
 import type { SceneObject } from '../model/SceneObject';
 import { flatListOf, listItemOf } from './listItems';
 import { FONT_KEY } from './fonts';
@@ -57,10 +58,14 @@ type Extras<K extends FlatKind> = K extends 'number'
 
 /** The definition of a flat kind: its default is a value of that kind, as the table says. */
 export type FlatDef<K extends FlatKind = FlatKind> = {
-  [P in K]: { key: string; label: string; kind: P; default: ValueOf<P> } & Extras<P>;
+  [P in K]: { key: string; label: string; kind: P; default: ValueOf<P>; scope?: Scope } & Extras<P>;
 }[K];
 
-/** The inspector is generated from these entries, so a new property is one line in a schema below. */
+/**
+ * The inspector is generated from these entries, so a new property is one line in a schema below.
+ * `scope` is only ever set on a behavior's own variables; the fixed schemas below leave it off, which
+ * reads as `local`.
+ */
 export type PropertyDef =
   | FlatDef
   /**
@@ -69,12 +74,19 @@ export type PropertyDef =
    * item kind: a list is stored in the project file, and an object is a live handle that no reload
    * survives.
    */
-  | { key: string; label: string; kind: 'list'; default: ListValue }
+  | { key: string; label: string; kind: 'list'; default: ListValue; scope?: Scope }
   /**
    * `fields` is the declaration; the value carries exactly those keys, which is what lets a struct
    * keep its shape while single fields are written (`mergeStruct`).
    */
-  | { key: string; label: string; kind: 'struct'; default: StructValue; fields: readonly StructFieldDef[] };
+  | {
+      key: string;
+      label: string;
+      kind: 'struct';
+      default: StructValue;
+      fields: readonly StructFieldDef[];
+      scope?: Scope;
+    };
 
 export interface PrimitiveFieldDef {
   key: string;
@@ -299,10 +311,15 @@ export function schemaForAsset(project: Project, asset: Asset): PropertySchema {
   return schemaForBag(project, asset, asset.props);
 }
 
-/** A placed object's rows: an object overriding its shader has that shader's parameters. */
+/**
+ * A placed object's rows: an object overriding its shader has that shader's parameters. A global
+ * variable is not among them – it belongs to the run, not to this object, so it shows no row here
+ * and never reaches `entity.props` (which is what lets the shared bag answer for it instead).
+ */
 export function schemaForObject(project: Project, asset: Asset, object: SceneObject): PropertySchema {
   const shader = object.overrides[SHADER_KEY];
-  return schemaForBag(project, asset, shader === undefined ? asset.props : { [SHADER_KEY]: shader });
+  const rows = schemaForBag(project, asset, shader === undefined ? asset.props : { [SHADER_KEY]: shader });
+  return rows.some(isGlobal) ? rows.filter((def) => !isGlobal(def)) : rows;
 }
 
 function schemaForBag(project: Project, asset: Asset, bag: PropertyBag): PropertySchema {
diff --git a/src/core/store/serialize.ts b/src/core/store/serialize.ts
index a572a9f1..6e43f672 100644
--- a/src/core/store/serialize.ts
+++ b/src/core/store/serialize.ts
@@ -14,7 +14,7 @@ import {
 } from '../graph';
 import { isParticleNodeDef } from '../particles/nodes';
 import { isShaderNodeDef } from '../shader/nodes';
-import type { Asset, TextureFrame } from '../model/Asset';
+import type { Asset, StateMachineAsset, TextureFrame } from '../model/Asset';
 import { isAssetType } from '../model/AssetTypes';
 import { isFontFile } from '../model/font';
 import { emptyEdit, type InstanceEdit, isEmptyEdit } from '../model/instance';
@@ -26,6 +26,7 @@ import {
   tagOf,
 } from '../model/Properties';
 import { PROJECT_FORMAT_VERSION, type Project } from '../model/Project';
+import { readScope } from '../model/Scope';
 import type { SceneObject } from '../model/SceneObject';
 import { isTextureFile, normalizeFrameRect } from '../model/texture';
 import { hasParentCycle } from '../model/walk';
@@ -130,7 +131,15 @@ export function deserializeProject(raw: unknown, fallbackId = ''): Project {
         graph: normalizeGraph(a.graph),
       });
     } else if (type === 'statemachine') {
-      assets.push({ id, type, name, props, graph: normalizeGraph(a.graph, (def) => def.type === STATE) });
+      const machine: StateMachineAsset = {
+        id,
+        type,
+        name,
+        props,
+        graph: normalizeGraph(a.graph, (def) => def.type === STATE),
+      };
+      if (readScope(a.scope) === 'global') machine.scope = 'global';
+      assets.push(machine);
     } else if (type === 'shader') {
       assets.push({ id, type, name, props, graph: shaderGraphs.get(id) ?? createEmptyGraph() });
     } else if (type === 'particles') {
@@ -251,6 +260,8 @@ function normalizeVariables(raw: unknown): PropertyDef[] {
     const fields = normalizeStructFields(v.fields);
     const def = variableDef(key, kind, undefined, fields);
     def.default = coerceValue(def, (v.default ?? def.default) as PropertyValue);
+    // Written only when shared, so every project made before scopes existed saves back unchanged.
+    if (readScope(v.scope) === 'global') def.scope = 'global';
     defs.push(def);
   }
   return defs;
diff --git a/src/editor/PlaySession.ts b/src/editor/PlaySession.ts
index 3bd77eee..3b4002d8 100644
--- a/src/editor/PlaySession.ts
+++ b/src/editor/PlaySession.ts
@@ -3,7 +3,7 @@
  * keyboard and the per-frame step. Play never touches the saved model – the world is built
  * from the runtime copy `state.enterPlay()` swaps in and `exitPlay()` throws away.
  */
-import { worldPositionOf } from '../core/graph';
+import { emptySharedState, type SharedState, worldPositionOf } from '../core/graph';
 import {
   addGameSystems,
   type BehaviorSystem,
@@ -33,6 +33,8 @@ export interface WorldSnapshot {
     props: Record<string, unknown>;
     animation: AnimationClock | null;
   }[];
+  /** What `global` declarations share this run – no entity carries it, so it is reported apart. */
+  shared: SharedState;
   log: string[];
 }
 
@@ -169,6 +171,7 @@ export class PlaySession {
           animation: e.animation ? { ...e.animation } : null,
         };
       }),
+      shared: this.behaviors?.shared ?? emptySharedState(),
       log: [...world.log],
     };
   }
diff --git a/src/editor/inspector/assetSection.ts b/src/editor/inspector/assetSection.ts
index 12965722..f23ff1d9 100644
--- a/src/editor/inspector/assetSection.ts
+++ b/src/editor/inspector/assetSection.ts
@@ -2,6 +2,7 @@ import {
   RenameAssetCommand,
   ResetAssetPropertyCommand,
   SetAssetPropertyCommand,
+  SetMachineScopeCommand,
 } from '../../core/commands/assetCommands';
 import { nextFieldName, nextVariableName } from '../../core/commands/naming';
 import {
@@ -11,10 +12,13 @@ import {
   RemoveVariableCommand,
   RenameStructFieldCommand,
   RenameVariableCommand,
+  SetVariableScopeCommand,
 } from '../../core/commands/variableCommands';
 import type { Command } from '../../core/commands/Command';
-import type { Asset, BehaviorAsset } from '../../core/model/Asset';
+import type { Asset, BehaviorAsset, StateMachineAsset } from '../../core/model/Asset';
+import { globalConflicts } from '../../core/graph/sharedState';
 import { findAsset, type Project } from '../../core/model/Project';
+import { isGlobal, type Scope, scopeOf } from '../../core/model/Scope';
 import { type StructFieldKind, VARIABLE_KINDS } from '../../core/properties/kinds';
 import { type PropertyDef, schemaForAsset, type StructFieldDef } from '../../core/properties/PropertySchema';
 import { markedAssetSchema } from '../../core/properties/deviation';
@@ -22,7 +26,7 @@ import { isModified, resolveAssetProps } from '../../core/properties/resolve';
 import { Dropdown, HStack, Label, Menu, Theme } from '../../ui';
 import { FontPreview } from '../font/FontPreview';
 import { aspectActions, sizeCommand } from './aspectAction';
-import { actionIf, createFieldRow, type FieldHandlers } from './fieldFactory';
+import { actionIf, createFieldRow, type FieldHandlers, NAME_WIDTH } from './fieldFactory';
 import { addNameField, addNote, addTitle, type InspectorHost } from './host';
 import { buildVariable, kindMenu, type VariableEditing } from './variableRows';
 import { listOpener, previewingHandlers, structFields } from './previewHandlers';
@@ -36,13 +40,16 @@ const newField = (key: string, kind: StructFieldKind): StructFieldDef => ({ key,
  */
 export function assetSignature(project: Project, assetId: string): string {
   const asset = findAsset(project, assetId);
-  return asset ? schemaForAsset(project, asset).map(defSignature).join(',') : 'missing';
+  if (!asset) return 'missing';
+  // A machine's own rows are none, so its scope has to be named here or switching it rebuilds nothing.
+  const machine = asset.type === 'statemachine' ? `|${scopeOf(asset)}` : '';
+  return schemaForAsset(project, asset).map(defSignature).join(',') + machine;
 }
 
 export function defSignature(def: PropertyDef): string {
   // Only a struct has rows of its own; a list is one row whatever its items are.
   const fields = def.kind === 'struct' ? def.fields.map((f) => `${f.key}:${f.kind}`).join('+') : '';
-  return `${def.key}:${def.kind}${fields ? `(${fields})` : ''}`;
+  return `${def.key}:${def.kind}${fields ? `(${fields})` : ''}@${scopeOf(def)}`;
 }
 
 /** Name, properties (asset values marked when they differ from the default) and, for behaviors, the variables. */
@@ -59,6 +66,7 @@ export function buildAssetSection(host: InspectorHost, assetId: string): void {
 
   buildProps(host, asset, markedAssetSchema(host.state.project, asset));
   if (asset.type === 'behavior') buildVariables(host, asset);
+  if (asset.type === 'statemachine') buildMachineScope(host, asset);
   // A font has no properties at all, so without this its inspector would be the name and nothing.
   if (asset.type === 'font')
     host.body.add(
@@ -152,6 +160,7 @@ function buildVariables(host: InspectorHost, asset: BehaviorAsset): void {
       remove: () => run(new RemoveVariableCommand(asset.id, def.key)),
       renameField: (field, next) => run(new RenameStructFieldCommand(asset.id, def.key, field.key, next)),
       removeField: (field) => run(new RemoveStructFieldCommand(asset.id, def.key, field.key)),
+      setScope: (scope) => run(new SetVariableScopeCommand(asset.id, def.key, scope)),
       addField: (kind) =>
         run(
           new AddStructFieldCommand(
@@ -164,4 +173,35 @@ function buildVariables(host: InspectorHost, asset: BehaviorAsset): void {
     const value = values[def.key] ?? def.default;
     host.fields.set(def.key, buildVariable(host, def, value, assetHandlers(host, asset.id, def), { edit }));
   }
+
+  // The mark alone says nothing to someone meeting it for the first time.
+  if (asset.variables.some(isGlobal))
+    addNote(host, '⊕ is one value for the whole run, shared by name.', 'small');
+
+  // A global name is shared with every other behavior declaring it, so the disagreement shows here.
+  const own = new Set(asset.variables.map((v) => v.key));
+  for (const conflict of globalConflicts(host.state.project))
+    if (own.has(conflict.key)) addNote(host, conflict.message, 'warning');
+}
+
+/** A state machine has no properties of its own, so the inspector shows just its name and this. */
+function buildMachineScope(host: InspectorHost, asset: StateMachineAsset): void {
+  const row = new HStack({ gap: Theme.gap, align: 'center' });
+  row.add(new Label('Scope', { style: 'muted', width: NAME_WIDTH, padding: Theme.fieldPadding }));
+  const pick = new Dropdown(isGlobal(asset) ? 'Global' : 'Local', { variant: 'ghost' });
+  const set = (scope: Scope) => () => void host.state.execute(new SetMachineScopeCommand(asset.id, scope));
+  pick.onClick = () =>
+    new Menu([
+      { label: 'Local \u2013 one current state per object', onSelect: set('local') },
+      { label: 'Global \u2013 one current state for the whole run', onSelect: set('global') },
+    ]).openBelow(pick);
+  row.add(pick, 1);
+  host.body.add(row);
+  addNote(
+    host,
+    isGlobal(asset)
+      ? 'Every behavior using this machine shares its current state.'
+      : 'Each behavior instance keeps its own current state.',
+    'small',
+  );
 }
diff --git a/src/editor/inspector/objectSection.ts b/src/editor/inspector/objectSection.ts
index 4e26e3cb..b9a7b77d 100644
--- a/src/editor/inspector/objectSection.ts
+++ b/src/editor/inspector/objectSection.ts
@@ -24,6 +24,7 @@ import {
 } from '../../core/model/instance';
 import type { PropertyValue } from '../../core/model/Properties';
 import { findAsset, findObjectHolder, type Project } from '../../core/model/Project';
+import { isGlobal } from '../../core/model/Scope';
 import type { SceneObject } from '../../core/model/SceneObject';
 import {
   COMMON_PROPS,
@@ -52,6 +53,17 @@ import { buildVariable } from './variableRows';
 import { currentProps, currentRef, deviations, positionMoved, targetOf, viewOf } from './objectQueries';
 import { componentRow, OFFSET_AXES, offsetKey, POSITION_AXES } from './vectorRows';
 
+/**
+ * The rows a placed object shows for what it was placed from: a behavior's declared variables, any
+ * other asset's schema minus the common switches. A global variable is none of them – it belongs to
+ * the run, so this object has no value of its own to show or override.
+ */
+export function objectRows(project: Project, asset: Asset, object: SceneObject): PropertyDef[] {
+  return asset.type === 'behavior'
+    ? asset.variables.filter((def) => !isGlobal(def))
+    : schemaForObject(project, asset, object).filter((def) => !isCommonProp(def.key));
+}
+
 /** Structure-defining facts of an object selection: parent, template link and schema. */
 export function objectSignature(
   project: Project,
@@ -186,14 +198,17 @@ export function buildObjectSection(host: InspectorHost, holderId: string, object
 
   // Asset properties (or behavior variables) with overrides; the switches are shown above.
   const values = resolveSceneObjectProps(host.state.project, asset, object);
-  const own =
-    asset.type === 'behavior'
-      ? asset.variables
-      : schemaForObject(host.state.project, asset, object).filter((def) => !isCommonProp(def.key));
+  const own = objectRows(host.state.project, asset, object);
   if (own.length > 0 || asset.type === 'behavior')
     addTitle(host, asset.type === 'behavior' ? 'VARIABLES' : 'PROPERTIES');
-  if (own.length === 0 && asset.type === 'behavior') addNote(host, 'The behavior declares no variables.');
+  // A global variable is missing from the rows above but not from the behavior, so saying it
+  // declares none would be untrue – name it instead, and where it went.
+  const shared = asset.type === 'behavior' ? asset.variables.filter(isGlobal) : [];
+  if (own.length === 0 && shared.length === 0 && asset.type === 'behavior')
+    addNote(host, 'The behavior declares no variables.');
   for (const def of own) propertyRow(host, holderId, objectId, asset, def, values, asset.type === 'behavior');
+  if (shared.length > 0)
+    addNote(host, `Shared by the whole run: ${shared.map((def) => def.key).join(', ')}.`, 'small');
   markObjectRows(host, object, asset, target);
 
   if (asset.type === 'container') contentSection(host, holderId, object, asset.objects.length);
diff --git a/src/editor/inspector/variableRows.ts b/src/editor/inspector/variableRows.ts
index 2dd0fe25..0542b93f 100644
--- a/src/editor/inspector/variableRows.ts
+++ b/src/editor/inspector/variableRows.ts
@@ -1,4 +1,5 @@
 import type { PropertyValue } from '../../core/model/Properties';
+import { type Scope, scopeOf } from '../../core/model/Scope';
 import { kindLabel, kindMark, STRUCT_FIELD_KINDS, type StructFieldKind } from '../../core/properties/kinds';
 import type { PropertyDef, StructDef, StructFieldDef } from '../../core/properties/PropertySchema';
 import {
@@ -39,11 +40,21 @@ export function kindMenu<K extends string>(kinds: readonly K[], pick: (kind: K)
 export interface VariableEditing {
   rename: (next: string) => void;
   remove: () => void;
+  setScope: (scope: Scope) => void;
   renameField: (field: StructFieldDef, next: string) => void;
   removeField: (field: StructFieldDef) => void;
   addField: (kind: StructFieldKind) => void;
 }
 
+const SCOPE_MARK: Record<Scope, string> = { local: '◦', global: '⊕' };
+
+function scopePicker(def: PropertyDef, edit: VariableEditing): Button {
+  return markPicker(SCOPE_MARK[scopeOf(def)], [
+    { label: 'Local – one value per object', onSelect: () => edit.setScope('local') },
+    { label: 'Global – one value for the whole run', onSelect: () => edit.setScope('global') },
+  ]);
+}
+
 export interface VariableOptions {
   edit?: VariableEditing;
   /** ↺/↑ on the first row: an override covers a whole struct, so its fields share them. */
@@ -71,6 +82,7 @@ export function buildVariable(
   } else {
     setValue = addValue(head, createField(host, def, value, handlers));
   }
+  if (edit) head.add(scopePicker(def, edit));
   if (edit) head.add(removeButton(edit.remove));
   const refreshActions = actions ? attachRowActions(head, actions) : () => {};
   host.body.add(head);
diff --git a/src/runtime/systems/BehaviorSystem.ts b/src/runtime/systems/BehaviorSystem.ts
index 167b8b43..637621db 100644
--- a/src/runtime/systems/BehaviorSystem.ts
+++ b/src/runtime/systems/BehaviorSystem.ts
@@ -1,11 +1,15 @@
 import {
   asNumber,
+  buildSharedState,
+  emptySharedState,
+  globalConflicts,
   type EntityHandle,
   type Graph,
   type GraphNode,
   GraphInterpreter,
   isHandleEnabled,
   type NodeContext,
+  type SharedState,
   type TraceListener,
   type Value,
 } from '../../core/graph';
@@ -83,6 +87,7 @@ export function behaviorError(world: World): string | undefined {
 export class BehaviorSystem implements System {
   private instances: Instance[] = [];
   private world: World | null = null;
+  private sharedState: SharedState = emptySharedState();
   private readonly collisions: CollisionSystem | null;
   private readonly animations: AnimationSystem | null;
 
@@ -100,9 +105,24 @@ export class BehaviorSystem implements System {
     this.animations = sources.animations ?? null;
   }
 
+  /** The values `global` declarations share this run – read-only to callers, rebuilt by `start`. */
+  get shared(): Readonly<SharedState> {
+    return this.sharedState;
+  }
+
   start(world: World): void {
     this.world = world;
     this.instances = [];
+    // Built fresh for every run: a shared variable starts at its declared value each time Play does.
+    this.sharedState = buildSharedState(this.project);
+    // Two behaviors declaring one global name with different kinds: whichever ran second would read
+    // a value of a type it never declared, so nothing runs until that is settled.
+    const blocking = globalConflicts(this.project).filter((c) => c.severity === 'error');
+    if (blocking.length > 0) {
+      for (const conflict of blocking) world.log.push(`${ERROR_PREFIX}: ${conflict.message}`);
+      world.stopRequested = true;
+      return;
+    }
     this.syncInstances(world);
   }
 
@@ -341,6 +361,7 @@ export class BehaviorSystem implements System {
       owner: entity.parent,
       variables: entity.props,
       states,
+      shared: this.sharedState,
       time: world.time,
       dt,
       findByName: (name) => world.findByName(name) ?? null,
diff --git a/tests/core/scope.test.ts b/tests/core/scope.test.ts
new file mode 100644
index 00000000..0d3544b5
--- /dev/null
+++ b/tests/core/scope.test.ts
@@ -0,0 +1,202 @@
+/**
+ * A variable or a state machine declared `global` keeps one value for the whole run instead of one
+ * per behavior instance. The name is the key: two behaviors declaring the same global name mean the
+ * same variable, while a behavior declaring it locally keeps its own.
+ */
+import { describe, expect, it } from 'vitest';
+import {
+  CreateAssetCommand,
+  SetAssetPropertyCommand,
+  SetMachineScopeCommand,
+} from '../../src/core/commands/assetCommands';
+import { AddNodeCommand, ConnectCommand } from '../../src/core/commands/graphCommands';
+import { AddVariableCommand, SetVariableScopeCommand } from '../../src/core/commands/variableCommands';
+import { globalConflicts, STATE, STATE_NAME_PARAM } from '../../src/core/graph';
+import type { BehaviorAsset } from '../../src/core/model/Asset';
+import type { PropertyValue } from '../../src/core/model/Properties';
+import type { VariableKind } from '../../src/core/properties/kinds';
+import { graphEditor, makeBehavior, makeSpriteScene, place, type SceneFixture, startWorld } from '../helpers';
+
+/** A behavior that adds one to `key` whenever it starts – the coin counter of the example game. */
+function makeCounter(fixture: SceneFixture, name: string, key: string, scope: 'local' | 'global') {
+  const behavior = makeBehavior(fixture, name, [key]);
+  if (scope === 'global') fixture.stack.execute(new SetVariableScopeCommand(behavior.id, key, scope));
+  const editor = graphEditor(fixture, behavior);
+  const start = editor.addNode('OnStart');
+  const read = editor.variables([key]);
+  const add = editor.addNode('Add', { b: 1 });
+  const write = editor.variables([key], { write: true });
+  editor.wire([
+    [start, 'exec', write, 'exec'],
+    [read, key, add, 'a'],
+    [add, 'result', write, key],
+  ]);
+  return behavior;
+}
+
+/** Places `count` objects of the behavior and runs one frame, so every `On start` has fired. */
+function runWith(fixture: SceneFixture, behaviors: readonly BehaviorAsset[]) {
+  for (const behavior of behaviors) place(fixture, behavior.id, { x: 0, y: 0 });
+  const started = startWorld(fixture, { behaviors: true });
+  started.frame();
+  return started;
+}
+
+describe('variable scope', () => {
+  it('counts once per instance when local', () => {
+    const f = makeSpriteScene();
+    const counter = makeCounter(f, 'Counter', 'score', 'local');
+    const started = runWith(f, [counter, counter]);
+    const values = started.world.entities.filter((e) => e.type === 'behavior').map((e) => e.props.score);
+    expect(values).toEqual([1, 1]);
+  });
+
+  it('counts once for the whole run when global', () => {
+    const f = makeSpriteScene();
+    const counter = makeCounter(f, 'Counter', 'score', 'global');
+    const started = runWith(f, [counter, counter]);
+    expect(started.behaviors!.shared.variables.score).toBe(2);
+    // The value belongs to the run, so it is no longer a property of any placed object.
+    for (const entity of started.world.entities) expect(entity.props.score).toBeUndefined();
+  });
+
+  it('shares one variable between two behaviors declaring the same global name', () => {
+    const f = makeSpriteScene();
+    const one = makeCounter(f, 'One', 'score', 'global');
+    const other = makeCounter(f, 'Other', 'score', 'global');
+    const started = runWith(f, [one, other]);
+    expect(started.behaviors!.shared.variables.score).toBe(2);
+  });
+
+  /** The scope sits on the declaration, so declaring the name yourself is how you opt out. */
+  it('lets a behavior declaring the name locally keep its own value', () => {
+    const f = makeSpriteScene();
+    const shared = makeCounter(f, 'Shared', 'score', 'global');
+    const own = makeCounter(f, 'Own', 'score', 'local');
+    const started = runWith(f, [shared, shared, own]);
+    expect(started.behaviors!.shared.variables.score).toBe(2);
+    const ownEntity = started.world.entities.find((e) => e.assetId === own.id)!;
+    expect(ownEntity.props.score).toBe(1);
+  });
+
+  it('starts a global variable at its declared value again on the next run', () => {
+    const f = makeSpriteScene();
+    const counter = makeCounter(f, 'Counter', 'score', 'global');
+    place(f, counter.id, { x: 0, y: 0 });
+    const first = startWorld(f, { behaviors: true });
+    first.frame();
+    expect(first.behaviors!.shared.variables.score).toBe(1);
+
+    const second = startWorld(f, { behaviors: true });
+    second.frame();
+    expect(second.behaviors!.shared.variables.score).toBe(1);
+  });
+});
+
+describe('two behaviors declaring the same global name', () => {
+  /** Declares `score` as `kind` with `start` as its value, global. */
+  function declare(fixture: SceneFixture, name: string, kind: VariableKind, start: PropertyValue) {
+    const behavior = makeBehavior(fixture, name);
+    fixture.stack.execute(new AddVariableCommand(behavior.id, 'score', kind));
+    fixture.stack.execute(new SetAssetPropertyCommand(behavior.id, 'score', start));
+    fixture.stack.execute(new SetVariableScopeCommand(behavior.id, 'score', 'global'));
+    return behavior;
+  }
+
+  it('refuses to run when the kinds disagree', () => {
+    const f = makeSpriteScene();
+    const counting = declare(f, 'Counting', 'number', 0);
+    declare(f, 'Naming', 'text', '');
+    place(f, counting.id, { x: 0, y: 0 });
+    const started = startWorld(f, { behaviors: true });
+
+    expect(started.world.stopRequested).toBe(true);
+    expect(started.world.log.join('\n')).toContain('is a number in Counting and a text in Naming');
+    expect(started.behaviors!.shared.variables.score).toBe(0);
+  });
+
+  it('runs on the first starting value when only the defaults disagree', () => {
+    const f = makeSpriteScene();
+    const first = declare(f, 'First', 'number', 7);
+    declare(f, 'Second', 'number', 99);
+    place(f, first.id, { x: 0, y: 0 });
+    const started = startWorld(f, { behaviors: true });
+    started.frame();
+
+    expect(started.world.stopRequested).toBe(false);
+    expect(started.behaviors!.shared.variables.score).toBe(7);
+    const conflicts = globalConflicts(f.project);
+    expect(conflicts.map((c) => c.severity)).toEqual(['warning']);
+    expect(conflicts[0]!.message).toContain('starts at 7 in First and at 99 in Second');
+  });
+
+  it('says nothing when they agree', () => {
+    const f = makeSpriteScene();
+    declare(f, 'First', 'number', 7);
+    declare(f, 'Second', 'number', 7);
+    expect(globalConflicts(f.project)).toEqual([]);
+  });
+});
+
+describe('state machine scope', () => {
+  /** A machine with one state, plus a behavior that enters it on start. */
+  function makeMachineAndSetter(fixture: SceneFixture, scope: 'local' | 'global') {
+    const machine = new CreateAssetCommand('statemachine', 'Doors');
+    fixture.stack.execute(machine);
+    const state = new AddNodeCommand(machine.asset.id, STATE, 0, 0, { [STATE_NAME_PARAM]: 'Open' });
+    fixture.stack.execute(state);
+    if (scope === 'global') fixture.stack.execute(new SetMachineScopeCommand(machine.asset.id, scope));
+
+    const behavior = makeBehavior(fixture, 'Opener');
+    const editor = graphEditor(fixture, behavior);
+    const start = editor.addNode('OnStart');
+    const set = editor.addNode('SetState', { machine: machine.asset.id });
+    fixture.stack.execute(
+      new ConnectCommand(
+        behavior.id,
+        { node: start.id, port: 'exec' },
+        { node: set.id, port: state.node.id },
+      ),
+    );
+    return { machineId: machine.asset.id, stateId: state.node.id, behavior };
+  }
+
+  /**
+   * A second behavior that never sets the state, only branches on it: it writes `sawOpen = 1` when
+   * the machine is already in Open. That is the whole difference a scope makes.
+   */
+  function makeReader(fixture: SceneFixture, machineId: string, stateId: string) {
+    const behavior = makeBehavior(fixture, 'Reader', ['sawOpen']);
+    const editor = graphEditor(fixture, behavior);
+    const start = editor.addNode('OnStart');
+    const branch = editor.addNode('StateBranch', { machine: machineId });
+    const one = editor.addNode('Add', { a: 1, b: 0 });
+    const write = editor.variables(['sawOpen'], { write: true });
+    editor.wire([
+      [start, 'exec', branch, 'exec'],
+      [branch, stateId, write, 'exec'],
+      [one, 'result', write, 'sawOpen'],
+    ]);
+    return behavior;
+  }
+
+  it('hides the state from another instance when local', () => {
+    const f = makeSpriteScene();
+    const { machineId, stateId, behavior } = makeMachineAndSetter(f, 'local');
+    const reader = makeReader(f, machineId, stateId);
+    const started = runWith(f, [behavior, reader]);
+    expect(started.behaviors!.shared.states[machineId]).toBeUndefined();
+    const seen = started.world.entities.find((e) => e.assetId === reader.id)!;
+    expect(seen.props.sawOpen).toBe(0);
+  });
+
+  it('shows the state to another instance when global', () => {
+    const f = makeSpriteScene();
+    const { machineId, stateId, behavior } = makeMachineAndSetter(f, 'global');
+    const reader = makeReader(f, machineId, stateId);
+    const started = runWith(f, [behavior, reader]);
+    expect(started.behaviors!.shared.states[machineId]).toBe(stateId);
+    const seen = started.world.entities.find((e) => e.assetId === reader.id)!;
+    expect(seen.props.sawOpen).toBe(1);
+  });
+});
diff --git a/tests/core/serialize.test.ts b/tests/core/serialize.test.ts
index 2e2de893..e6dc08f2 100644
--- a/tests/core/serialize.test.ts
+++ b/tests/core/serialize.test.ts
@@ -1,7 +1,12 @@
 import { describe, expect, it } from 'vitest';
-import { SetAssetPropertyCommand } from '../../src/core/commands/assetCommands';
+import {
+  CreateAssetCommand,
+  SetAssetPropertyCommand,
+  SetMachineScopeCommand,
+} from '../../src/core/commands/assetCommands';
 import { SetOverrideCommand } from '../../src/core/commands/sceneObjectCommands';
-import { deserializeProject } from '../../src/core/store/serialize';
+import { SetVariableScopeCommand } from '../../src/core/commands/variableCommands';
+import { deserializeProject, serializeProject } from '../../src/core/store/serialize';
 import { makeBehavior, makeSpriteScene, place, roundTrip } from '../helpers';
 
 describe('serialize', () => {
@@ -21,6 +26,40 @@ describe('serialize', () => {
     expect(loaded.props.runInEditor).toBe(true);
   });
 
+  it('round-trips the scope of a variable and of a state machine', () => {
+    const f = makeSpriteScene();
+    const behavior = makeBehavior(f, 'B', ['score']);
+    f.stack.execute(new SetVariableScopeCommand(behavior.id, 'score', 'global'));
+    const machine = new CreateAssetCommand('statemachine', 'M');
+    f.stack.execute(machine);
+    f.stack.execute(new SetMachineScopeCommand(machine.asset.id, 'global'));
+    expect(roundTrip(f.project)).toEqual(f.project);
+  });
+
+  /** `local` is the absence of the field, so a project made before scopes existed saves back byte-alike. */
+  it('writes no scope for a local variable and reads an unknown one as local', () => {
+    const f = makeSpriteScene();
+    const behavior = makeBehavior(f, 'B', ['score']);
+    expect(JSON.stringify(serializeProject(f.project))).not.toContain('scope');
+
+    const loaded = deserializeProject({
+      assets: [
+        {
+          id: behavior.id,
+          type: 'behavior',
+          name: 'B',
+          variables: [{ key: 'score', kind: 'number', scope: 'planet' }],
+        },
+        { id: 'm1', type: 'statemachine', name: 'M', scope: 'planet' },
+      ],
+    });
+    const reloaded = loaded.assets[0]!;
+    const machine = loaded.assets[1]!;
+    if (reloaded.type !== 'behavior' || machine.type !== 'statemachine') throw new Error('wrong types');
+    expect(reloaded.variables[0]!.scope).toBeUndefined();
+    expect(machine.scope).toBeUndefined();
+  });
+
   it('repairs broken documents', () => {
     const project = deserializeProject(
       {
diff --git a/tests/editor/object-variables.test.ts b/tests/editor/object-variables.test.ts
new file mode 100644
index 00000000..c4bef39d
--- /dev/null
+++ b/tests/editor/object-variables.test.ts
@@ -0,0 +1,27 @@
+/**
+ * What the inspector of a *placed* behavior lists. A global variable has no value of this object's
+ * own, so it gets no row here – the switch on the declaration is the only place it is edited.
+ */
+import { describe, expect, it } from 'vitest';
+import { SetVariableScopeCommand } from '../../src/core/commands/variableCommands';
+import { findAsset } from '../../src/core/model/Project';
+import { objectRows } from '../../src/editor/inspector/objectSection';
+import { makeBehavior, makeSpriteScene, place } from '../helpers';
+
+describe('the rows of a placed behavior', () => {
+  it('lists a local variable and leaves out a global one', () => {
+    const f = makeSpriteScene();
+    const behavior = makeBehavior(f, 'Counter', ['score', 'lives']);
+    const objectId = place(f, behavior.id, { x: 0, y: 0 });
+    const rows = () => {
+      const asset = findAsset(f.project, behavior.id)!;
+      return objectRows(f.project, asset, f.object(objectId)).map((def) => def.key);
+    };
+
+    expect(rows()).toEqual(['score', 'lives']);
+    f.stack.execute(new SetVariableScopeCommand(behavior.id, 'score', 'global'));
+    expect(rows()).toEqual(['lives']);
+    f.stack.undo();
+    expect(rows()).toEqual(['score', 'lives']);
+  });
+});
diff --git a/tests/editor/variable-rows.test.ts b/tests/editor/variable-rows.test.ts
index 77d81fdc..102fcf7d 100644
--- a/tests/editor/variable-rows.test.ts
+++ b/tests/editor/variable-rows.test.ts
@@ -44,6 +44,7 @@ const withFields: FieldHandlers = { ...noHandlers(), structFieldHandlers: noHand
 const EDIT: VariableEditing = {
   rename: () => {},
   remove: () => {},
+  setScope: () => {},
   renameField: () => {},
   removeField: () => {},
   addField: () => {},
diff --git a/tests/helpers.ts b/tests/helpers.ts
index da966538..e9a2f863 100644
--- a/tests/helpers.ts
+++ b/tests/helpers.ts
@@ -7,6 +7,7 @@ import { requireNodeDef } from '../src/core/commands/require';
 import { AddVariableCommand } from '../src/core/commands/variableCommands';
 import {
   type DeclaredPort,
+  emptySharedState,
   ENTITY_HANDLE,
   type EntityHandle,
   type GraphLookup,
@@ -185,6 +186,7 @@ export function fakeContext(overrides: Partial<NodeContext> = {}): FakeContext {
     owner: fakeEntity('owner'),
     variables: { speed: 100 },
     states: {},
+    shared: emptySharedState(),
     time: 0,
     dt: 0.5,
     logs,
diff --git a/tools/e2e/32-scope.mjs b/tools/e2e/32-scope.mjs
new file mode 100644
index 00000000..bcbbc76b
--- /dev/null
+++ b/tools/e2e/32-scope.mjs
@@ -0,0 +1,166 @@
+import { edge, node, port, variable, written } from '../lib/builders.mjs';
+import { MAKE_OBJECT } from './lib/scaffold.mjs';
+
+/**
+ * Scopes: a variable or a state machine declared `global` keeps one value for the whole run instead
+ * of one per behavior instance. The step checks the run (two objects counting into one number), the
+ * switch in the inspector, and that a global variable stops being a property of the placed object.
+ *
+ * The step brings its own boxes, behavior and machine; everything it adds is removed at the end.
+ */
+
+/** `On start → Variables{set score} ← Add(score, 1)`: every instance adds one to the same number. */
+const counterGraph = {
+  nodes: [
+    node('sc-start', 'OnStart', 0, 0),
+    node('sc-read', 'Variables', 0, 200, {}, [port('score', 'number')]),
+    node('sc-add', 'Add', 260, 200, { b: 1 }),
+    node('sc-write', 'Variables', 560, 0, {}, [written('score', 'number')]),
+  ],
+  edges: [
+    edge('sc-e1', 'sc-start', 'exec', 'sc-write', 'exec'),
+    edge('sc-e2', 'sc-read', 'score', 'sc-add', 'a'),
+    edge('sc-e3', 'sc-add', 'result', 'sc-write', 'score'),
+  ],
+};
+
+const globalScore = { ...variable('score', 'number', 0), scope: 'global' };
+
+export async function scope(t) {
+  const { check, sleep, evaluate, json, shot, click, locate, asset, mutate, stop, has } = t;
+
+  const selectAsset = async (id) => {
+    await evaluate(`__gm.state.select({ kind: 'asset', assetId: ${JSON.stringify(id)} })`);
+    await sleep(300);
+  };
+  const selectObject = async (id) => {
+    await evaluate(
+      `__gm.state.select({ kind: 'object', holderId: __gm.state.activeScene.id, objectId: ${JSON.stringify(id)} })`,
+    );
+    await sleep(300);
+  };
+  /** The inspector is drawn over the graph, so the last match is the row rather than a port. */
+  const clickLast = async (text) => {
+    const p = await locate(text, true);
+    await click(p.x, p.y);
+    await sleep(250);
+  };
+  const scopeOfVariable = async () => (await asset('sc-logic')).variables[0].scope ?? 'local';
+
+  // 32a. Two boxes wearing one behavior whose `score` is global.
+  await mutate(`
+    const p = __gm.state.project;
+    const scene = __gm.state.activeScene;
+    const mover = p.assets.find((a) => a.id === 'mover');
+    const a = structuredClone(mover);
+    Object.assign(a, {
+      id: 'sc-logic',
+      name: 'Counter',
+      props: { enabled: true, runInEditor: false, score: 0 },
+      variables: ${JSON.stringify([globalScore])},
+      graph: ${JSON.stringify(counterGraph)},
+    });
+    p.assets.unshift(a);
+    ${MAKE_OBJECT}
+    scene.objects.push(
+      make('sc-box-a', 'crate', '', 1500, 'Counter box A'),
+      make('sc-brain-a', 'sc-logic', 'sc-box-a', 0, 'Counter A'),
+      make('sc-box-b', 'crate', '', 1700, 'Counter box B'),
+      make('sc-brain-b', 'sc-logic', 'sc-box-b', 0, 'Counter B'),
+    );
+  `);
+  await sleep(400);
+
+  // 32b. The run: two instances, one number. A per-instance variable would stand at 1.
+  await t.play();
+  await sleep(600);
+  const world = await json('__gm.world()');
+  const carriers = world.entities.filter((e) => e.props && 'score' in e.props).map((e) => e.name);
+  check(
+    'two behavior instances count into one global variable',
+    world.shared.variables.score === 2,
+    `score = ${JSON.stringify(world.shared.variables.score)} after both started – 1 would mean each kept its own`,
+  );
+  check(
+    'and the value belongs to the run, not to either placed object',
+    carriers.length === 0,
+    `objects carrying "score": ${JSON.stringify(carriers)}`,
+  );
+  await stop();
+  await sleep(400);
+
+  // 32c. A global variable shows no row on the object placed from the behavior – overriding one
+  //      value of something every object shares would mean nothing.
+  await selectObject('sc-brain-a');
+  const rowWhileGlobal = await has('score');
+  const saysWhereItWent = await has('Shared by the whole run: score.');
+  check(
+    'the object names the variable it no longer holds, instead of claiming there is none',
+    saysWhereItWent && !(await has('The behavior declares no variables.')),
+    `note found: ${saysWhereItWent}`,
+  );
+  await shot('01-object-without-global');
+
+  // 32d. The switch sits on the declaration, in the behavior's own inspector.
+  await selectAsset('sc-logic');
+  const picker = await locate('⊕');
+  check(
+    'a global variable is marked as shared where it is declared',
+    Boolean(picker),
+    JSON.stringify(picker),
+  );
+  await shot('02-declaration');
+  await click(picker.x, picker.y);
+  await sleep(250);
+  await clickLast('Local – one value per object');
+  await sleep(350);
+  check(
+    'and the menu switches it back to one value per object',
+    (await scopeOfVariable()) === 'local',
+    `scope is now ${await scopeOfVariable()}`,
+  );
+
+  await selectObject('sc-brain-a');
+  const rowWhileLocal = await has('score');
+  check(
+    'the row appears on the placed object exactly while the variable is local',
+    !rowWhileGlobal && rowWhileLocal,
+    `global: ${rowWhileGlobal}, local: ${rowWhileLocal}`,
+  );
+
+  // 32e. A machine carries the same switch, and its own inspector is where it lives.
+  await mutate(`
+    const p = __gm.state.project;
+    p.assets.unshift({
+      id: 'sc-machine',
+      type: 'statemachine',
+      name: 'Shared doors',
+      props: {},
+      graph: { nodes: [], edges: [] },
+    });
+  `);
+  await selectAsset('sc-machine');
+  const machineScope = await has('Local');
+  const pick = await locate('Local', true);
+  await click(pick.x, pick.y);
+  await sleep(250);
+  await clickLast('Global – one current state for the whole run');
+  await sleep(350);
+  const machine = await asset('sc-machine');
+  check(
+    'a state machine is switched between one current state per object and one for the run',
+    machineScope && machine.scope === 'global',
+    `dropdown found: ${machineScope}, scope now ${JSON.stringify(machine.scope)}`,
+  );
+  await shot('03-machine-scope');
+
+  // 32f. Everything this step added goes again.
+  await mutate(`
+    const p = __gm.state.project;
+    const scene = __gm.state.activeScene;
+    scene.objects = scene.objects.filter((o) => !o.id.startsWith('sc-'));
+    p.assets = p.assets.filter((a) => !a.id.startsWith('sc-'));
+    __gm.state.select(null);
+  `);
+  await sleep(300);
+}
diff --git a/tools/e2e/index.mjs b/tools/e2e/index.mjs
index c9f6dde1..37e5d87f 100644
--- a/tools/e2e/index.mjs
+++ b/tools/e2e/index.mjs
@@ -34,6 +34,7 @@ import { shader } from './28-shader.mjs';
 import { transform } from './29-transform.mjs';
 import { font } from './30-font.mjs';
 import { particles } from './31-particles.mjs';
+import { scope } from './32-scope.mjs';
 
 export const STEPS = [
   hierarchy,
@@ -67,4 +68,5 @@ export const STEPS = [
   transform,
   font,
   particles,
+  scope,
 ];