googleapis
diff --git a/google/cloud/pubsub_v1/subscriber/client.py b/google/cloud/pubsub_v1/subscriber/client.py
@@ -223,7 +223,8 @@ def callback(message):
                 inundated with too many messages at once.
             scheduler (~google.cloud.pubsub_v1.subscriber.scheduler.Scheduler): An optional
                 *scheduler* to use when executing the callback. This controls
-                how callbacks are executed concurrently.
+                how callbacks are executed concurrently. This object must not be shared
+                across multiple SubscriberClients.
 
         Returns:
             A :class:`~google.cloud.pubsub_v1.subscriber.futures.StreamingPullFuture`

diff --git a/google/cloud/pubsub_v1/subscriber/scheduler.py b/google/cloud/pubsub_v1/subscriber/scheduler.py
@@ -74,7 +74,8 @@ def _make_default_thread_pool_executor():
 
 
 class ThreadScheduler(Scheduler):
-    """A thread pool-based scheduler.
+    """A thread pool-based scheduler. It must not be shared across
+       SubscriberClients.
 
     This scheduler is useful in typical I/O-bound message processing.