diff --git a/docs/specs/game-clock/tasks.md b/docs/specs/game-clock/tasks.md
index 60abd5b..e5d5882 100644
--- a/docs/specs/game-clock/tasks.md
+++ b/docs/specs/game-clock/tasks.md
@@ -2,7 +2,7 @@
 
 Work through the tasks in order; each ends with its tests passing and a commit. Tick a task when it is committed.
 
-- [ ] 1. **Core types and helpers**: `GameClock`, `CLOCK_LOW_TIME_MS`, the new optional fields on `Game`,
+- [x] 1. **Core types and helpers**: `GameClock`, `CLOCK_LOW_TIME_MS`, the new optional fields on `Game`,
       `GameEndMessage`, `MoveRecord` and `FinishedGameSummary`; `getClockTimes`, `ClockSync`, `getClockAtMove`,
       `formatClock` with unit tests; English timeout texts.
 - [ ] 2. **Clock in the game lifecycle**: `GameClock.ts`, `GAME_CLOCK_MS`, `clock` and `moveRemainingMs` on
diff --git a/packages/core/src/clock/Clock.ts b/packages/core/src/clock/Clock.ts
new file mode 100644
index 0000000..aef42f2
--- /dev/null
+++ b/packages/core/src/clock/Clock.ts
@@ -0,0 +1,83 @@
+import { Game } from "../models/Game";
+import { ClockTimes, GameClock, Seat } from "../models/GameClock";
+import { GameRecord } from "../models/GameHistory";
+
+export interface ClockState extends ClockTimes {
+    // Undefined when no clock runs.
+    runningSeat?: Seat;
+}
+
+export function getSeat(players: { player1Id: string, player2Id: string }, playerId: string): Seat | undefined {
+    if (playerId === players.player1Id) return "player1";
+    if (playerId === players.player2Id) return "player2";
+    return undefined;
+}
+
+// Both players' time at `now` (server time); never below zero.
+export function getClockTimes(clock: GameClock, runningSeat: Seat | undefined, now: number): ClockTimes {
+    const elapsed = runningSeat && clock.turnStartedAt !== undefined ? Math.max(0, now - clock.turnStartedAt) : 0;
+    return {
+        player1Ms: Math.max(0, clock.player1Ms - (runningSeat === "player1" ? elapsed : 0)),
+        player2Ms: Math.max(0, clock.player2Ms - (runningSeat === "player2" ? elapsed : 0)),
+    };
+}
+
+// "4:59"; rounded up, so "0:00" only shows when the time is gone.
+export function formatClock(milliseconds: number): string {
+    const seconds = Math.ceil(Math.max(0, milliseconds) / 1000);
+    return `${Math.floor(seconds / 60)}:${String(seconds % 60).padStart(2, "0")}`;
+}
+
+type ClockRecord = Pick<GameRecord, "clockInitialMs" | "moves" | "player1" | "result" | "endReason">;
+
+// Both players' time after the given move of a saved game; move 0 is the start. Undefined for games saved before
+// the game clock.
+export function getClockAtMove(record: ClockRecord, moveNumber: number): ClockTimes | undefined {
+    if (record.clockInitialMs === undefined) return undefined;
+    const n = Math.min(Math.max(moveNumber, 0), record.moves.length);
+    const times: ClockTimes = { player1Ms: record.clockInitialMs, player2Ms: record.clockInitialMs };
+    for (const move of record.moves.slice(0, n)) {
+        if (move.remainingMs === undefined) continue;
+        if (move.playerId === record.player1.userId) times.player1Ms = move.remainingMs;
+        else times.player2Ms = move.remainingMs;
+    }
+    // The player who ran out of time did not get to move again; their clock ends at zero.
+    if (n === record.moves.length && record.endReason === "timeout" && record.result !== null) {
+        if (record.result === "player1") times.player2Ms = 0;
+        if (record.result === "player2") times.player1Ms = 0;
+    }
+    return times;
+}
+
+// Follows the clock of a live game from the server's messages and counts down between them, in server time.
+export class ClockSync {
+    private clock?: GameClock;
+    private runningSeat?: Seat;
+    // Server time minus local time.
+    private offsetMs = 0;
+
+    // From a live game message (game start, update, reconnect).
+    update(game: Game, receivedAt = Date.now()) {
+        const { mancalaGame } = game;
+        this.clock = game.clock;
+        this.runningSeat = mancalaGame.state === "ended" ? undefined : getSeat(mancalaGame, mancalaGame.turnPlayerId);
+        if (game.serverTime !== undefined) this.offsetMs = game.serverTime - receivedAt;
+    }
+
+    // When the game has ended; the server sends the stopped clocks.
+    stop(clock?: GameClock) {
+        if (clock) this.clock = clock;
+        this.runningSeat = undefined;
+    }
+
+    get isRunning(): boolean {
+        return this.clock?.turnStartedAt !== undefined && this.runningSeat !== undefined;
+    }
+
+    // Undefined when the server sends no clock.
+    getTimes(now = Date.now()): ClockState | undefined {
+        if (!this.clock) return undefined;
+        const runningSeat = this.isRunning ? this.runningSeat : undefined;
+        return { ...getClockTimes(this.clock, runningSeat, now + this.offsetMs), runningSeat };
+    }
+}
diff --git a/packages/core/src/clock/index.ts b/packages/core/src/clock/index.ts
new file mode 100644
index 0000000..9b8b971
--- /dev/null
+++ b/packages/core/src/clock/index.ts
@@ -0,0 +1 @@
+export * from './Clock'
diff --git a/packages/core/src/index.ts b/packages/core/src/index.ts
index 5e3baca..72c074e 100644
--- a/packages/core/src/index.ts
+++ b/packages/core/src/index.ts
@@ -9,3 +9,4 @@ export * from './factory/index'
 export * from './viewmodel/index'
 export * from './service/index'
 export * from './history/index'
+export * from './clock/index'
diff --git a/packages/core/src/localization/en.ts b/packages/core/src/localization/en.ts
index 8b2e101..12c08a9 100644
--- a/packages/core/src/localization/en.ts
+++ b/packages/core/src/localization/en.ts
@@ -54,8 +54,8 @@ export const en = {
     Draw: "Draw",
     OpponentLeft: "Opponent left",
     YouLeft: "You left",
-    OpponentTimedOut: "Opponent timed out",
-    YouTimedOut: "You timed out",
+    OpponentTimedOut: "Opponent ran out of time",
+    YouTimedOut: "You ran out of time",
     Abandoned: "Abandoned",
     PlayerWon: "{{name}} won",
     Moves: "Moves",
diff --git a/packages/core/src/models/Game.ts b/packages/core/src/models/Game.ts
index 7a0a2bb..bc496a6 100644
--- a/packages/core/src/models/Game.ts
+++ b/packages/core/src/models/Game.ts
@@ -1,4 +1,5 @@
 import { MancalaGame } from "mancala.js";
+import { GameClock } from "./GameClock";
 import { UserConnectionInfo } from "./UserConnectionInfo";
 
 export interface Game {
@@ -9,6 +10,10 @@ export interface Game {
     startedAt?: number;
     // Time of each move, aligned with mancalaGame.history.
     moveTimes?: number[];
+    // Sent by servers with a game clock.
+    clock?: GameClock;
+    // Server time (epoch milliseconds) when the message was built, so clients can correct for their own clock.
+    serverTime?: number;
 }
 
 export interface GameUsersConnectionInfo {
diff --git a/packages/core/src/models/GameClock.ts b/packages/core/src/models/GameClock.ts
new file mode 100644
index 0000000..059c211
--- /dev/null
+++ b/packages/core/src/models/GameClock.ts
@@ -0,0 +1,20 @@
+// Below this, the running clock is shown as low on time.
+export const CLOCK_LOW_TIME_MS = 30_000;
+
+export type Seat = "player1" | "player2";
+
+// The players' clocks in a live game. The server keeps the time; clients only display it.
+export interface GameClock {
+    // Time each player started the game with.
+    initialMs: number;
+    // Time left for each player. For the player whose turn it is, at turnStartedAt.
+    player1Ms: number;
+    player2Ms: number;
+    // Server time (epoch milliseconds) when the running clock started; undefined when no clock runs.
+    turnStartedAt?: number;
+}
+
+export interface ClockTimes {
+    player1Ms: number;
+    player2Ms: number;
+}
diff --git a/packages/core/src/models/GameHistory.ts b/packages/core/src/models/GameHistory.ts
index 9460093..516ffb0 100644
--- a/packages/core/src/models/GameHistory.ts
+++ b/packages/core/src/models/GameHistory.ts
@@ -1,4 +1,5 @@
 import { GameStep } from "mancala.js";
+import { GameClock } from "./GameClock";
 
 // How long the player whose turn it is may stay offline before the opponent wins.
 export const TURN_TIMEOUT_MS = 5 * 60 * 1000;
@@ -20,6 +21,8 @@ export interface MoveRecord {
     gameSteps: GameStep[];
     // Epoch milliseconds.
     at: number;
+    // The mover's clock after the move; undefined for games saved before the game clock.
+    remainingMs?: number;
 }
 
 export type GameResult = "player1" | "player2" | "draw";
@@ -51,6 +54,8 @@ export interface FinishedGameSummary {
     endedAt: number;
     moveCount: number;
     peakSpectators: number;
+    // Time each player started with; undefined for games saved before the game clock.
+    clockInitialMs?: number;
 }
 
 export interface GameRecord extends FinishedGameSummary {
@@ -72,4 +77,6 @@ export interface GameEndMessage {
     endReason: EndReason;
     winnerId?: string;
     leftUserId?: string;
+    // The stopped clocks.
+    clock?: GameClock;
 }
diff --git a/packages/core/src/models/index.ts b/packages/core/src/models/index.ts
index 8e274b5..408e5bb 100644
--- a/packages/core/src/models/index.ts
+++ b/packages/core/src/models/index.ts
@@ -5,3 +5,4 @@ export * from './User'
 export * from './UserConnectionInfo'
 export * from './AuthUser'
 export * from './GameHistory'
+export * from './GameClock'
diff --git a/packages/core/tests/clock/Clock.test.ts b/packages/core/tests/clock/Clock.test.ts
new file mode 100644
index 0000000..4c01529
--- /dev/null
+++ b/packages/core/tests/clock/Clock.test.ts
@@ -0,0 +1,136 @@
+import { CommonMancalaGame } from "mancala.js";
+import { ClockSync, formatClock, getClockAtMove, getClockTimes } from "../../src/clock";
+import { Game, GameClock, GameRecord, MoveRecord } from "../../src/models";
+
+const P1 = "player-1";
+const P2 = "player-2";
+const MINUTE = 60_000;
+
+const clock = (overrides: Partial<GameClock> = {}): GameClock =>
+    ({ initialMs: 5 * MINUTE, player1Ms: 5 * MINUTE, player2Ms: 5 * MINUTE, turnStartedAt: 1_000_000, ...overrides });
+
+const liveGame = (turnPlayerId: string, gameClock: GameClock | undefined, serverTime?: number): Game => {
+    const mancalaGame = new CommonMancalaGame("game-1", P1, P2);
+    mancalaGame.turnPlayerId = turnPlayerId;
+    return {
+        id: "game-1",
+        mancalaGame,
+        gameUsersConnectionInfo: {
+            user1ConnectionInfo: { userId: P1, isOnline: true },
+            user2ConnectionInfo: { userId: P2, isOnline: true },
+        },
+        clock: gameClock,
+        serverTime,
+    };
+};
+
+const move = (playerId: string, remainingMs?: number): MoveRecord =>
+    ({ playerId, moveIndex: 0, boardSnapshot: [], gameSteps: [], at: 0, remainingMs });
+
+const record = (overrides: Partial<GameRecord>): GameRecord => ({
+    id: "game-1",
+    player1: { userId: P1, isGuest: true },
+    player2: { userId: P2, isGuest: true },
+    board: [],
+    result: "player1",
+    endReason: "completed",
+    startedAt: 0,
+    endedAt: 0,
+    moveCount: 0,
+    peakSpectators: 0,
+    totalSpectators: 0,
+    moves: [],
+    clockInitialMs: 5 * MINUTE,
+    ...overrides,
+});
+
+describe("getClockTimes", () => {
+    it("deducts the time since the turn started from the running seat only", () => {
+        expect(getClockTimes(clock(), "player1", 1_000_000 + 20_000)).toEqual({ player1Ms: 280_000, player2Ms: 300_000 });
+        expect(getClockTimes(clock(), "player2", 1_000_000 + 20_000)).toEqual({ player1Ms: 300_000, player2Ms: 280_000 });
+    });
+
+    it("does not count down when no clock runs", () => {
+        expect(getClockTimes(clock({ turnStartedAt: undefined }), "player1", 5_000_000)).toEqual({ player1Ms: 300_000, player2Ms: 300_000 });
+        expect(getClockTimes(clock(), undefined, 5_000_000)).toEqual({ player1Ms: 300_000, player2Ms: 300_000 });
+    });
+
+    it("never goes below zero", () => {
+        expect(getClockTimes(clock({ player1Ms: 1_000 }), "player1", 1_000_000 + 60_000).player1Ms).toBe(0);
+    });
+});
+
+describe("formatClock", () => {
+    it("shows minutes and seconds, rounding up", () => {
+        expect(formatClock(300_000)).toBe("5:00");
+        expect(formatClock(299_001)).toBe("5:00");
+        expect(formatClock(299_000)).toBe("4:59");
+        expect(formatClock(9_500)).toBe("0:10");
+        expect(formatClock(1)).toBe("0:01");
+        expect(formatClock(0)).toBe("0:00");
+        expect(formatClock(-5)).toBe("0:00");
+    });
+});
+
+describe("ClockSync", () => {
+    it("counts down the running clock in server time, whatever the local clock says", () => {
+        const sync = new ClockSync();
+        const localTimeAtReceive = 1_000_000 + 10 * MINUTE; // the device clock is 10 minutes fast
+        sync.update(liveGame(P2, clock({ turnStartedAt: 1_000_000 }), 1_000_000 + 5_000), localTimeAtReceive);
+
+        expect(sync.isRunning).toBe(true);
+        expect(sync.getTimes(localTimeAtReceive)).toEqual({ player1Ms: 300_000, player2Ms: 295_000, runningSeat: "player2" });
+        expect(sync.getTimes(localTimeAtReceive + 3_000)).toEqual({ player1Ms: 300_000, player2Ms: 292_000, runningSeat: "player2" });
+    });
+
+    it("stops with the clocks the server sends when the game ends", () => {
+        const sync = new ClockSync();
+        sync.update(liveGame(P1, clock(), 1_000_000), 1_000_000);
+        sync.stop(clock({ player1Ms: 0, turnStartedAt: undefined }));
+
+        expect(sync.isRunning).toBe(false);
+        expect(sync.getTimes(9_000_000)).toEqual({ player1Ms: 0, player2Ms: 300_000, runningSeat: undefined });
+    });
+
+    it("does not run once the game has ended", () => {
+        const game = liveGame(P1, clock(), 1_000_000);
+        game.mancalaGame.state = "ended";
+        const sync = new ClockSync();
+        sync.update(game, 1_000_000);
+
+        expect(sync.isRunning).toBe(false);
+        expect(sync.getTimes(2_000_000)?.player1Ms).toBe(300_000);
+    });
+
+    it("has no times when the server sends no clock", () => {
+        const sync = new ClockSync();
+        sync.update(liveGame(P1, undefined), 0);
+        expect(sync.getTimes()).toBeUndefined();
+        expect(sync.isRunning).toBe(false);
+    });
+});
+
+describe("getClockAtMove", () => {
+    const moves = [move(P1, 290_000), move(P2, 280_000), move(P2, 270_000), move(P1, 250_000)];
+
+    it("starts with the initial time", () => {
+        expect(getClockAtMove(record({ moves }), 0)).toEqual({ player1Ms: 300_000, player2Ms: 300_000 });
+    });
+
+    it("shows each player's time after their last move so far", () => {
+        expect(getClockAtMove(record({ moves }), 1)).toEqual({ player1Ms: 290_000, player2Ms: 300_000 });
+        expect(getClockAtMove(record({ moves }), 3)).toEqual({ player1Ms: 290_000, player2Ms: 270_000 });
+        expect(getClockAtMove(record({ moves }), 4)).toEqual({ player1Ms: 250_000, player2Ms: 270_000 });
+        expect(getClockAtMove(record({ moves }), 99)).toEqual({ player1Ms: 250_000, player2Ms: 270_000 });
+    });
+
+    it("shows the player who ran out of time at zero in the final position", () => {
+        const timedOut = record({ moves, endReason: "timeout", result: "player1" });
+        expect(getClockAtMove(timedOut, 4)).toEqual({ player1Ms: 250_000, player2Ms: 0 });
+        expect(getClockAtMove(timedOut, 3)).toEqual({ player1Ms: 290_000, player2Ms: 270_000 });
+    });
+
+    it("is undefined for games saved before the game clock", () => {
+        expect(getClockAtMove(record({ moves: [move(P1)], clockInitialMs: undefined }), 1)).toBeUndefined();
+    });
+});