diff --git a/docker/models/containers.py b/docker/models/containers.py
index 9644b002..42c9d556 100644
--- a/docker/models/containers.py
+++ b/docker/models/containers.py
@@ -152,7 +152,8 @@ class Container(Model):
         Returns:
             (tuple): A tuple of (exit_code, output)
                 exit_code: (int):
-                    Exit code for the executed command
+                    Exit code for the executed command or ``None`` if
+                    either ``stream```or ``socket`` is ``True``.
                 output: (generator or str):
                     If ``stream=True``, a generator yielding response chunks.
                     If ``socket=True``, a socket object for the connection.
@@ -170,10 +171,11 @@ class Container(Model):
         exec_output = self.client.api.exec_start(
             resp['Id'], detach=detach, tty=tty, stream=stream, socket=socket
         )
-        exit_code = 0
-        if stream is False:
-            exit_code = self.client.api.exec_inspect(resp['Id'])['ExitCode']
-        return (exit_code, exec_output)
+        if socket or stream:
+            return None, exec_output
+        else:
+            return (self.client.api.exec_inspect(resp['Id'])['ExitCode'],
+                    exec_output)
 
     def export(self):
         """