diff --git a/Lib/test/test_threading.py b/Lib/test/test_threading.py
--- a/Lib/test/test_threading.py
+++ b/Lib/test/test_threading.py
@@ -1042,6 +1042,37 @@
         self.assertEqual(out, b'')
         self.assertNotIn("Unhandled exception", err.decode())

+    def test_sys_exit_stderr(self):
+        # Documentation states that sys.exit(arg) writes
+        # arg to stderr, as long as it is not an integer
+        # or None. Ensure that this statement is true
+        # when sys.exit() is called from within threads
+        # other than the main thread. See issue 6634.
+        template = r"""if True:
+            import sys, threading
+            def run():
+                %s
+            t = threading.Thread(target=run)
+            t.start()
+            t.join()
+            """
+
+        script = template % 'sys.exit("error message")'
+        rc, out, err = assert_python_ok("-c", script)
+        self.assertEqual(err.decode(), "error message")
+
+        script = template % 'sys.exit(None)'
+        rc, out, err = assert_python_ok("-c", script)
+        self.assertEqual(err, b'')
+
+        script = template % 'sys.exit(1)'
+        rc, out, err = assert_python_ok("-c", script)
+        self.assertEqual(err, b'')
+
+        script = template % 'raise SystemExit("error message")'
+        rc, out, err = assert_python_ok("-c", script)
+        self.assertEqual(err.decode(), "error message")
+

 class TimerTests(BaseTestCase):

diff --git a/Lib/threading.py b/Lib/threading.py
--- a/Lib/threading.py
+++ b/Lib/threading.py
@@ -921,8 +921,16 @@

             try:
                 self.run()
-            except SystemExit:
-                pass
+            except SystemExit as e:
+                # Handle "exit code" (provided via argument to SystemExit, if
+                # raised manually, or via argument to sys.exit()). Ignore None
+                # and integer. Attempt to write any other object to stderr, as
+                # is the behavior of sys.exit() called from the main thread.
+                if e.args:
+                    code = e.args[0]
+                    if code is not None and not isinstance(code, int):
+                        if _sys and _sys.stderr is not None:
+                            print(code, file=_sys.stderr)
             except:
                 # If sys.stderr is no more (most likely from interpreter
                 # shutdown) use self._stderr.  Otherwise still use sys (as in