diff --git a/Lib/test/_test_multiprocessing.py b/Lib/test/_test_multiprocessing.py
index b720a483e9b..bfaa02b0fcc 100644
--- a/Lib/test/_test_multiprocessing.py
+++ b/Lib/test/_test_multiprocessing.py
@@ -2799,16 +2799,17 @@ class _TestMyManager(BaseTestCase):
         self.common(manager)
         manager.shutdown()
 
-        # If the manager process exited cleanly then the exitcode
-        # will be zero.  Otherwise (after a short timeout)
-        # terminate() is used, resulting in an exitcode of -SIGTERM.
-        self.assertEqual(manager._process.exitcode, 0)
+        # bpo-30356: BaseManager._finalize_manager() sends SIGTERM
+        # to the manager process if it takes longer than 1 second to stop,
+        # which happens on slow buildbots.
+        self.assertIn(manager._process.exitcode, (0, -signal.SIGTERM))
 
     def test_mymanager_context(self):
         with MyManager() as manager:
             self.common(manager)
         # bpo-30356: BaseManager._finalize_manager() sends SIGTERM
-        # to the manager process if it takes longer than 1 second to stop.
+        # to the manager process if it takes longer than 1 second to stop,
+        # which happens on slow buildbots.
         self.assertIn(manager._process.exitcode, (0, -signal.SIGTERM))
 
     def test_mymanager_context_prestarted(self):
diff --git a/Misc/NEWS.d/next/Tests/2019-09-24-12-30-55.bpo-37123.IoutBn.rst b/Misc/NEWS.d/next/Tests/2019-09-24-12-30-55.bpo-37123.IoutBn.rst
new file mode 100644
index 00000000000..200a5c324d6
--- /dev/null
+++ b/Misc/NEWS.d/next/Tests/2019-09-24-12-30-55.bpo-37123.IoutBn.rst
@@ -0,0 +1,4 @@
+Multiprocessing test test_mymanager() now also expects -SIGTERM, not only
+exitcode 0. BaseManager._finalize_manager() sends SIGTERM to the manager
+process if it takes longer than 1 second to stop, which happens on slow
+buildbots.