diff --git a/CHANGELOG.md b/CHANGELOG.md
index 4fcf7b9a..7688486d 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -2,6 +2,15 @@
 
 ## [Unreleased]
 
+### Phase 6 — streaming agent loop (2026-06-14)
+
+Phase 6 **AI-037, slice a** — the loop streams its steps so the reader can watch the agent work. The SSE endpoint + run persistence + `GET` are slice b.
+
+- **`AgentLoop.StreamAsync`** — yields an `AgentEvent` per step as it happens (`llm_response` / `tool_result`), then a terminal Done event carrying the final `AgentResult`. `RunAsync` is now built on top of it (collects to the Done result), so non-streaming callers (the AI-039 eval) are unchanged — behaviour identical, budget exhaustion still throws with its transcript after the partial steps have streamed.
+- **`AgentEvent`** (`Ai.Agents`) — a step-or-result union (`OfStep`/`Done`).
+- **`StudyBuddyAgent.StreamAsync`** — same prompt/tools/budget as `RunAsync`, streamed; both share one `BuildAgentInput`.
+- Tests: `AgentLoop.StreamAsync` (step events in order → terminal Done; budget exhaustion streams partial steps then throws, no Done); `StudyBuddyAgent.StreamAsync` (config threading → step + Done). Full suite green (270).
+
 ### Phase 6 — agent run persistence (2026-06-14)
 
 Phase 6 **AI-036** — agent runs are saved so the reader UI can replay an agent's steps (AI-038) and runs are observable. Persistence mechanics only; the endpoint that calls it is AI-037.
diff --git a/backend/src/Ai/TextStack.Ai.Agents/AgentLoop.cs b/backend/src/Ai/TextStack.Ai.Agents/AgentLoop.cs
index c18f86de..0a4b60f9 100644
--- a/backend/src/Ai/TextStack.Ai.Agents/AgentLoop.cs
+++ b/backend/src/Ai/TextStack.Ai.Agents/AgentLoop.cs
@@ -1,10 +1,21 @@
 using System.Diagnostics;
+using System.Runtime.CompilerServices;
 using System.Text.Json;
 using TextStack.Ai.Core;
 using TextStack.Ai.Tools;
 
 namespace TextStack.Ai.Agents;
 
+/// <summary>
+/// One event from a streamed agent run (AI-037a): either a recorded <see cref="Step"/> as it happens,
+/// or the terminal <see cref="Result"/>. Exactly one is non-null.
+/// </summary>
+public sealed record AgentEvent(AgentStep? Step, AgentResult<string>? Result)
+{
+    public static AgentEvent OfStep(AgentStep step) => new(step, null);
+    public static AgentEvent Done(AgentResult<string> result) => new(null, result);
+}
+
 /// <summary>
 /// The hand-rolled plan → act → observe loop (Phase 6, AI-034) every concrete agent runs on. Each
 /// iteration: ask the model (with the agent's allowed tool schemas); if it answers without a tool
@@ -18,8 +29,32 @@ namespace TextStack.Ai.Agents;
 /// </summary>
 public sealed class AgentLoop(ILlmService llm, IToolRegistry tools, ToolDispatcher dispatcher)
 {
+    /// <summary>
+    /// Runs the loop to completion and returns the final result. Built on <see cref="StreamAsync"/> —
+    /// for non-streaming callers (e.g. the eval, AI-039). Budget exhaustion still throws
+    /// <see cref="AgentBudgetExhaustedException"/> (with its transcript).
+    /// </summary>
     public async Task<AgentResult<string>> RunAsync(
         AgentInput input, AgentContext ctx, AgentLoopOptions options, CancellationToken ct)
+    {
+        await foreach (var e in StreamAsync(input, ctx, options, ct))
+        {
+            if (e.Result is { } result)
+                return result;
+        }
+        // Unreachable: the loop either yields a Done event or throws on budget exhaustion.
+        throw new InvalidOperationException("Agent stream ended without a result.");
+    }
+
+    /// <summary>
+    /// Streams the run step-by-step (AI-037a): an <see cref="AgentEvent"/> per recorded step as it
+    /// happens, then a terminal Done event carrying the final <see cref="AgentResult{T}"/>. The
+    /// endpoint (AI-037b) maps these to SSE so the reader sees the agent's progress. Budget exhaustion
+    /// throws after the partial steps have already streamed.
+    /// </summary>
+    public async IAsyncEnumerable<AgentEvent> StreamAsync(
+        AgentInput input, AgentContext ctx, AgentLoopOptions options,
+        [EnumeratorCancellation] CancellationToken ct)
     {
         var sw = Stopwatch.StartNew();
         var steps = new List<AgentStep>();
@@ -42,15 +77,19 @@ public async Task<AgentResult<string>> RunAsync(
             inputTokens += response.Usage.InputTokens;
             outputTokens += response.Usage.OutputTokens;
             cost += response.Usage.CostUsd;
-            steps.Add(Step(iteration, "llm_response", SerializeResponse(response)));
+
+            var llmStep = Step(iteration, "llm_response", SerializeResponse(response));
+            steps.Add(llmStep);
+            yield return AgentEvent.OfStep(llmStep);
 
             // No tool calls → the model has produced its final answer.
             if (response.ToolCalls.Count == 0)
             {
                 sw.Stop();
-                return new AgentResult<string>(
+                yield return AgentEvent.Done(new AgentResult<string>(
                     response.Text, steps,
-                    new AgentUsage(iteration + 1, inputTokens, outputTokens, cost, (int)sw.ElapsedMilliseconds));
+                    new AgentUsage(iteration + 1, inputTokens, outputTokens, cost, (int)sw.ElapsedMilliseconds)));
+                yield break;
             }
 
             // The assistant's tool-call turn must precede the tool results (OpenAI message ordering).
@@ -61,7 +100,9 @@ public async Task<AgentResult<string>> RunAsync(
             {
                 var call = response.ToolCalls[j];
                 var result = results[j];
-                steps.Add(Step(iteration, "tool_result", SerializeResult(call, result)));
+                var toolStep = Step(iteration, "tool_result", SerializeResult(call, result));
+                steps.Add(toolStep);
+                yield return AgentEvent.OfStep(toolStep);
                 // Errors come back as data (ToolCallingSession serialization) so the model can recover.
                 messages.Add(new LlmMessage("tool", ToolCallingSession.SerializeResult(result), [call]));
             }
diff --git a/backend/src/Application/Agents/StudyBuddyAgent.cs b/backend/src/Application/Agents/StudyBuddyAgent.cs
index ec2e1c8b..3a91b2aa 100644
--- a/backend/src/Application/Agents/StudyBuddyAgent.cs
+++ b/backend/src/Application/Agents/StudyBuddyAgent.cs
@@ -31,16 +31,15 @@ public sealed class StudyBuddyAgent(AgentLoop loop) : IAgent<StudyBuddyInput, st
         "get_user_highlights",
     ];
 
-    public Task<AgentResult<string>> RunAsync(StudyBuddyInput input, AgentContext ctx, CancellationToken ct)
-    {
-        var agentInput = new AgentInput(
-            UserGoal: BuildGoal(input),
-            SystemPrompt: SystemPrompt,
-            AllowedTools: AllowedTools,
-            FeatureTag: FeatureTag);
+    public Task<AgentResult<string>> RunAsync(StudyBuddyInput input, AgentContext ctx, CancellationToken ct) =>
+        loop.RunAsync(BuildAgentInput(input), ctx, Options, ct);
 
-        return loop.RunAsync(agentInput, ctx, Options, ct);
-    }
+    /// <summary>Streams the run step-by-step (AI-037a) for the SSE endpoint — same config as <see cref="RunAsync"/>.</summary>
+    public IAsyncEnumerable<AgentEvent> StreamAsync(StudyBuddyInput input, AgentContext ctx, CancellationToken ct) =>
+        loop.StreamAsync(BuildAgentInput(input), ctx, Options, ct);
+
+    private static AgentInput BuildAgentInput(StudyBuddyInput input) =>
+        new(UserGoal: BuildGoal(input), SystemPrompt: SystemPrompt, AllowedTools: AllowedTools, FeatureTag: FeatureTag);
 
     private static string BuildGoal(StudyBuddyInput input)
     {
diff --git a/tests/TextStack.UnitTests/AgentLoopTests.cs b/tests/TextStack.UnitTests/AgentLoopTests.cs
index c9a2a956..84410cf0 100644
--- a/tests/TextStack.UnitTests/AgentLoopTests.cs
+++ b/tests/TextStack.UnitTests/AgentLoopTests.cs
@@ -133,6 +133,46 @@ await Assert.ThrowsAsync<AgentBudgetExhaustedException>(() =>
                 TestContext.Current.CancellationToken));
     }
 
+    [Fact]
+    public async Task Stream_EmitsStepEventsThenTerminalDone()
+    {
+        var llm = new ScriptedLlm(
+            [Call(args: """{"x":1}""")], // turn 1: tool
+            ["Final."]);                  // turn 2: answer
+        var events = new List<AgentEvent>();
+        await foreach (var e in Loop(llm, new EchoTool()).StreamAsync(
+            Input(), Ctx(), new AgentLoopOptions(), TestContext.Current.CancellationToken))
+        {
+            events.Add(e);
+        }
+
+        // step (llm) → step (tool) → step (llm) → done; exactly one terminal result.
+        Assert.Equal(3, events.Count(e => e.Step is not null));
+        var done = Assert.Single(events.Where(e => e.Result is not null));
+        Assert.Equal("Final.", done.Result!.Output);
+        Assert.Equal(2, done.Result.Usage.Iterations);
+        Assert.Same(events[^1], done); // done is the last event
+    }
+
+    [Fact]
+    public async Task Stream_BudgetExhausted_StreamsPartialSteps_ThenThrows()
+    {
+        var llm = new ScriptedLlm([Call()], [Call()], [Call()]); // never answers
+        var streamed = new List<AgentEvent>();
+
+        await Assert.ThrowsAsync<AgentBudgetExhaustedException>(async () =>
+        {
+            await foreach (var e in Loop(llm, new EchoTool()).StreamAsync(
+                Input(), Ctx(), new AgentLoopOptions(MaxSteps: 3), TestContext.Current.CancellationToken))
+            {
+                streamed.Add(e);
+            }
+        });
+
+        Assert.NotEmpty(streamed);                          // partial steps reached the consumer
+        Assert.All(streamed, e => Assert.Null(e.Result));   // no Done event on exhaustion
+    }
+
     [Fact]
     public async Task Run_UnknownTool_FedBackAsData_LoopRecovers()
     {
diff --git a/tests/TextStack.UnitTests/StudyBuddyAgentTests.cs b/tests/TextStack.UnitTests/StudyBuddyAgentTests.cs
index 5b0003e3..769e289b 100644
--- a/tests/TextStack.UnitTests/StudyBuddyAgentTests.cs
+++ b/tests/TextStack.UnitTests/StudyBuddyAgentTests.cs
@@ -57,6 +57,26 @@ public async Task Run_FeedsPromptAndPassageGoal_ReturnsAnswer()
         Assert.Contains("Chapter 3", request.Messages[0].Content); // chapter threaded into the goal
     }
 
+    [Fact]
+    public async Task Stream_FeedsSameConfig_EmitsStepThenDone()
+    {
+        var llm = new FixedLlm("Streamed explanation.");
+        var agent = new StudyBuddyAgent(Loop(llm));
+
+        var events = new List<AgentEvent>();
+        await foreach (var e in agent.StreamAsync(
+            new StudyBuddyInput("A confusing passage.", Guid.NewGuid(), ChapterNumber: 2),
+            Ctx(), TestContext.Current.CancellationToken))
+        {
+            events.Add(e);
+        }
+
+        var done = Assert.Single(events.Where(e => e.Result is not null));
+        Assert.Equal("Streamed explanation.", done.Result!.Output);
+        Assert.Equal(StudyBuddyAgent.SystemPrompt, llm.Requests[0].SystemPrompt);
+        Assert.Contains("Chapter 2", llm.Requests[0].Messages[0].Content);
+    }
+
     [Fact]
     public async Task Run_NoChapter_GoalOmitsChapter()
     {