diff --git a/dom/media/webaudio/AudioContext.cpp b/dom/media/webaudio/AudioContext.cpp
index 9e411fa254ab7..976ae1c778b44 100644
--- a/dom/media/webaudio/AudioContext.cpp
+++ b/dom/media/webaudio/AudioContext.cpp
@@ -126,11 +126,15 @@ AudioContext::AudioContext(nsPIDOMWindowInner* aWindow,
 nsresult
 AudioContext::Init()
 {
+  // We skip calling SetIsOnlyNodeForContext and the creation of the
+  // audioChannelAgent during mDestination's constructor, because we can only
+  // call them after mDestination has been set up.
   if (!mIsOffline) {
     nsresult rv = mDestination->CreateAudioChannelAgent();
     if (NS_WARN_IF(NS_FAILED(rv))) {
       return rv;
     }
+    mDestination->SetIsOnlyNodeForContext(true);
   }
 
   return NS_OK;
@@ -678,7 +682,8 @@ double
 AudioContext::CurrentTime() const
 {
   MediaStream* stream = Destination()->Stream();
-  return stream->StreamTimeToSeconds(stream->GetCurrentTime());
+  return stream->StreamTimeToSeconds(stream->GetCurrentTime() +
+                                     Destination()->ExtraCurrentTime());
 }
 
 void
@@ -988,6 +993,13 @@ AudioContext::RegisterNode(AudioNode* aNode)
 {
   MOZ_ASSERT(!mAllNodes.Contains(aNode));
   mAllNodes.PutEntry(aNode);
+  // mDestinationNode may be null when we're destroying nodes unlinked by CC.
+  // Skipping unnecessary calls after shutdown avoids RunInStableState events
+  // getting stuck in CycleCollectedJSRuntime during final cycle collection
+  // (bug 1200514).
+  if (mDestination && !mIsShutDown) {
+    mDestination->SetIsOnlyNodeForContext(mAllNodes.Count() == 1);
+  }
 }
 
 void
@@ -995,6 +1007,10 @@ AudioContext::UnregisterNode(AudioNode* aNode)
 {
   MOZ_ASSERT(mAllNodes.Contains(aNode));
   mAllNodes.RemoveEntry(aNode);
+  // mDestinationNode may be null when we're destroying nodes unlinked by CC
+  if (mDestination) {
+    mDestination->SetIsOnlyNodeForContext(mAllNodes.Count() == 1);
+  }
 }
 
 JSObject*
diff --git a/dom/media/webaudio/AudioDestinationNode.cpp b/dom/media/webaudio/AudioDestinationNode.cpp
index b455d4d6edc0e..7da9c5dd901b2 100644
--- a/dom/media/webaudio/AudioDestinationNode.cpp
+++ b/dom/media/webaudio/AudioDestinationNode.cpp
@@ -332,6 +332,8 @@ AudioDestinationNode::AudioDestinationNode(AudioContext* aContext,
   , mAudioChannel(AudioChannel::Normal)
   , mIsOffline(aIsOffline)
   , mAudioChannelAgentPlaying(false)
+  , mExtraCurrentTimeSinceLastStartedBlocking(0)
+  , mExtraCurrentTimeUpdatedSinceLastStableState(false)
   , mCaptured(false)
 {
   MediaStreamGraph* graph = aIsOffline ?
@@ -646,6 +648,73 @@ AudioDestinationNode::CreateAudioChannelAgent()
   return NS_OK;
 }
 
+void
+AudioDestinationNode::NotifyStableState()
+{
+  mExtraCurrentTimeUpdatedSinceLastStableState = false;
+}
+
+void
+AudioDestinationNode::ScheduleStableStateNotification()
+{
+  // Dispatch will fail if this is called on AudioNode destruction during
+  // shutdown, in which case failure can be ignored.
+  nsContentUtils::RunInStableState(NewRunnableMethod(this,
+                                                     &AudioDestinationNode::NotifyStableState));
+}
+
+StreamTime
+AudioDestinationNode::ExtraCurrentTime()
+{
+  if (!mStartedBlockingDueToBeingOnlyNode.IsNull() &&
+      !mExtraCurrentTimeUpdatedSinceLastStableState) {
+    mExtraCurrentTimeUpdatedSinceLastStableState = true;
+    // Round to nearest processing block.
+    double seconds =
+      (TimeStamp::Now() - mStartedBlockingDueToBeingOnlyNode).ToSeconds();
+    mExtraCurrentTimeSinceLastStartedBlocking = WEBAUDIO_BLOCK_SIZE *
+      StreamTime(seconds * Context()->SampleRate() / WEBAUDIO_BLOCK_SIZE + 0.5);
+    ScheduleStableStateNotification();
+  }
+  return mExtraCurrentTimeSinceLastStartedBlocking;
+}
+
+void
+AudioDestinationNode::SetIsOnlyNodeForContext(bool aIsOnlyNode)
+{
+  if (!mStartedBlockingDueToBeingOnlyNode.IsNull() == aIsOnlyNode) {
+    // Nothing changed.
+    return;
+  }
+
+  if (!mStream) {
+    // DestroyMediaStream has been called, presumably during CC Unlink().
+    return;
+  }
+
+  if (mIsOffline) {
+    // Don't block the destination stream for offline AudioContexts, since
+    // we expect the zero data produced when there are no other nodes to
+    // show up in its result buffer. Also, we would get confused by adding
+    // ExtraCurrentTime before StartRendering has even been called.
+    return;
+  }
+
+  if (aIsOnlyNode) {
+    mStream->Suspend();
+    mStartedBlockingDueToBeingOnlyNode = TimeStamp::Now();
+    // Don't do an update of mExtraCurrentTimeSinceLastStartedBlocking until the next stable state.
+    mExtraCurrentTimeUpdatedSinceLastStableState = true;
+    ScheduleStableStateNotification();
+  } else {
+    // Force update of mExtraCurrentTimeSinceLastStartedBlocking if necessary
+    ExtraCurrentTime();
+    mStream->AdvanceAndResume(mExtraCurrentTimeSinceLastStartedBlocking);
+    mExtraCurrentTimeSinceLastStartedBlocking = 0;
+    mStartedBlockingDueToBeingOnlyNode = TimeStamp();
+  }
+}
+
 void
 AudioDestinationNode::InputMuted(bool aMuted)
 {
diff --git a/dom/media/webaudio/AudioDestinationNode.h b/dom/media/webaudio/AudioDestinationNode.h
index 708cd1cc6e5aa..1def00a8714d3 100644
--- a/dom/media/webaudio/AudioDestinationNode.h
+++ b/dom/media/webaudio/AudioDestinationNode.h
@@ -65,6 +65,13 @@ class AudioDestinationNode final : public AudioNode
   void NotifyMainThreadStreamFinished() override;
   void FireOfflineCompletionEvent();
 
+  // An amount that should be added to the MediaStream's current time to
+  // get the AudioContext.currentTime.
+  StreamTime ExtraCurrentTime();
+
+  // When aIsOnlyNode is true, this is the only node for the AudioContext.
+  void SetIsOnlyNodeForContext(bool aIsOnlyNode);
+
   nsresult CreateAudioChannelAgent();
   void DestroyAudioChannelAgent();
 
@@ -94,6 +101,9 @@ class AudioDestinationNode final : public AudioNode
 
   void SetCanPlay(float aVolume, bool aMuted);
 
+  void NotifyStableState();
+  void ScheduleStableStateNotification();
+
   SelfReference<AudioDestinationNode> mOfflineRenderingRef;
   uint32_t mFramesToProduce;
 
@@ -107,6 +117,9 @@ class AudioDestinationNode final : public AudioNode
   bool mIsOffline;
   bool mAudioChannelAgentPlaying;
 
+  TimeStamp mStartedBlockingDueToBeingOnlyNode;
+  StreamTime mExtraCurrentTimeSinceLastStartedBlocking;
+  bool mExtraCurrentTimeUpdatedSinceLastStableState;
   bool mCaptured;
 };