diff --git a/RELEASENOTES.md b/RELEASENOTES.md
index f5353a24e1c..6f45ddcf93e 100644
--- a/RELEASENOTES.md
+++ b/RELEASENOTES.md
@@ -1,5 +1,11 @@
 # Release notes
 
+### 2.13.1 (not yet released)
+
+*   Core library:
+    *   Fix playback issue for HLS live streams without program date time
+        information ([#8560](https://github.com/google/ExoPlayer/issues/8560)).
+
 ### 2.13.0 (2021-02-04)
 
 *   Core library:
diff --git a/library/core/src/main/java/com/google/android/exoplayer2/ExoPlayerImplInternal.java b/library/core/src/main/java/com/google/android/exoplayer2/ExoPlayerImplInternal.java
index 755d7511c4e..f791d05b132 100644
--- a/library/core/src/main/java/com/google/android/exoplayer2/ExoPlayerImplInternal.java
+++ b/library/core/src/main/java/com/google/android/exoplayer2/ExoPlayerImplInternal.java
@@ -880,7 +880,7 @@ private void updatePlaybackPositions() throws ExoPlaybackException {
     // Adjust live playback speed to new position.
     if (playbackInfo.playWhenReady
         && playbackInfo.playbackState == Player.STATE_READY
-        && isCurrentPeriodInMovingLiveWindow()
+        && shouldUseLivePlaybackSpeedControl(playbackInfo.timeline, playbackInfo.periodId)
         && playbackInfo.playbackParameters.speed == 1f) {
       float adjustedSpeed =
           livePlaybackSpeedControl.getAdjustedPlaybackSpeed(
@@ -1051,17 +1051,14 @@ private long getLiveOffsetUs(Timeline timeline, Object periodUid, long periodPos
         - (periodPositionUs + period.getPositionInWindowUs());
   }
 
-  private boolean isCurrentPeriodInMovingLiveWindow() {
-    return isInMovingLiveWindow(playbackInfo.timeline, playbackInfo.periodId);
-  }
-
-  private boolean isInMovingLiveWindow(Timeline timeline, MediaPeriodId mediaPeriodId) {
+  private boolean shouldUseLivePlaybackSpeedControl(
+      Timeline timeline, MediaPeriodId mediaPeriodId) {
     if (mediaPeriodId.isAd() || timeline.isEmpty()) {
       return false;
     }
     int windowIndex = timeline.getPeriodByUid(mediaPeriodId.periodUid, period).windowIndex;
     timeline.getWindow(windowIndex, window);
-    return window.isLive() && window.isDynamic;
+    return window.isLive() && window.isDynamic && window.windowStartTimeMs != C.TIME_UNSET;
   }
 
   private void scheduleNextWork(long thisOperationStartTimeMs, long intervalMs) {
@@ -1725,7 +1722,7 @@ private boolean shouldTransitionToReadyState(boolean renderersReadyOrEnded) {
     }
     // Renderers are ready and we're loading. Ask the LoadControl whether to transition.
     long targetLiveOffsetUs =
-        isInMovingLiveWindow(playbackInfo.timeline, queue.getPlayingPeriod().info.id)
+        shouldUseLivePlaybackSpeedControl(playbackInfo.timeline, queue.getPlayingPeriod().info.id)
             ? livePlaybackSpeedControl.getTargetLiveOffsetUs()
             : C.TIME_UNSET;
     MediaPeriodHolder loadingHolder = queue.getLoadingPeriod();
@@ -1831,7 +1828,7 @@ private void updateLivePlaybackSpeedControl(
       Timeline oldTimeline,
       MediaPeriodId oldPeriodId,
       long positionForTargetOffsetOverrideUs) {
-    if (newTimeline.isEmpty() || !isInMovingLiveWindow(newTimeline, newPeriodId)) {
+    if (newTimeline.isEmpty() || !shouldUseLivePlaybackSpeedControl(newTimeline, newPeriodId)) {
       // Live playback speed control is unused.
       return;
     }
diff --git a/library/core/src/test/java/com/google/android/exoplayer2/ExoPlayerTest.java b/library/core/src/test/java/com/google/android/exoplayer2/ExoPlayerTest.java
index 008d8c6b537..e743858875a 100644
--- a/library/core/src/test/java/com/google/android/exoplayer2/ExoPlayerTest.java
+++ b/library/core/src/test/java/com/google/android/exoplayer2/ExoPlayerTest.java
@@ -71,6 +71,7 @@
 import com.google.android.exoplayer2.source.MediaSource.MediaPeriodId;
 import com.google.android.exoplayer2.source.MediaSourceEventListener;
 import com.google.android.exoplayer2.source.SilenceMediaSource;
+import com.google.android.exoplayer2.source.SinglePeriodTimeline;
 import com.google.android.exoplayer2.source.TrackGroup;
 import com.google.android.exoplayer2.source.TrackGroupArray;
 import com.google.android.exoplayer2.source.ads.AdPlaybackState;
@@ -83,6 +84,7 @@
 import com.google.android.exoplayer2.testutil.FakeAdaptiveDataSet;
 import com.google.android.exoplayer2.testutil.FakeAdaptiveMediaSource;
 import com.google.android.exoplayer2.testutil.FakeChunkSource;
+import com.google.android.exoplayer2.testutil.FakeClock;
 import com.google.android.exoplayer2.testutil.FakeDataSource;
 import com.google.android.exoplayer2.testutil.FakeMediaClockRenderer;
 import com.google.android.exoplayer2.testutil.FakeMediaPeriod;
@@ -8833,6 +8835,42 @@ public void targetLiveOffsetInMedia_withSetPlaybackParameters_usesPlaybackParame
     assertThat(liveOffsetAtEnd).isIn(Range.closed(1_900L, 2_100L));
   }
 
+  @Test
+  public void targetLiveOffsetInMedia_unknownWindowStartTime_doesNotAdjustLiveOffset()
+      throws Exception {
+    FakeClock fakeClock = new AutoAdvancingFakeClock(/* initialTimeMs= */ 987_654_321L);
+    ExoPlayer player = new TestExoPlayerBuilder(context).setClock(fakeClock).build();
+    MediaItem mediaItem =
+        new MediaItem.Builder().setUri(Uri.EMPTY).setLiveTargetOffsetMs(4_000).build();
+    Timeline liveTimeline =
+        new SinglePeriodTimeline(
+            /* presentationStartTimeMs= */ C.TIME_UNSET,
+            /* windowStartTimeMs= */ C.TIME_UNSET,
+            /* elapsedRealtimeEpochOffsetMs= */ C.TIME_UNSET,
+            /* periodDurationUs= */ 1000 * C.MICROS_PER_SECOND,
+            /* windowDurationUs= */ 1000 * C.MICROS_PER_SECOND,
+            /* windowPositionInPeriodUs= */ 0,
+            /* windowDefaultStartPositionUs= */ 0,
+            /* isSeekable= */ true,
+            /* isDynamic= */ true,
+            /* manifest= */ null,
+            mediaItem,
+            mediaItem.liveConfiguration);
+    player.pause();
+    player.setMediaSource(new FakeMediaSource(liveTimeline));
+    player.prepare();
+    TestPlayerRunHelper.runUntilPlaybackState(player, Player.STATE_READY);
+
+    long playbackStartTimeMs = fakeClock.elapsedRealtime();
+    TestPlayerRunHelper.playUntilPosition(player, /* windowIndex= */ 0, /* positionMs= */ 999_000);
+    long playbackEndTimeMs = fakeClock.elapsedRealtime();
+    player.release();
+
+    // Assert that the time it took to play 999 seconds of media is 999 seconds (asserting that no
+    // playback speed adjustment was used).
+    assertThat(playbackEndTimeMs - playbackStartTimeMs).isEqualTo(999_000);
+  }
+
   @Test
   public void noTargetLiveOffsetInMedia_doesNotAdjustLiveOffset() throws Exception {
     long windowStartUnixTimeMs = 987_654_321_000L;