diff --git a/Lib/test/test_logging.py b/Lib/test/test_logging.py
index 8356e6b..1a5f8b6 100644
--- a/Lib/test/test_logging.py
+++ b/Lib/test/test_logging.py
@@ -5190,6 +5190,13 @@ def test_should_not_rollover(self):
                 self.fn, encoding="utf-8", maxBytes=0)
         self.assertFalse(rh.shouldRollover(None))
         rh.close()
+        # bpo-45401 - test with special file
+        # We set maxBytes to 1 so that rollover would normally happen, except
+        # for the check for regular files
+        rh = logging.handlers.RotatingFileHandler(
+                os.devnull, encoding="utf-8", maxBytes=1)
+        self.assertFalse(rh.shouldRollover(self.next_rec()))
+        rh.close()
 
     def test_should_rollover(self):
         rh = logging.handlers.RotatingFileHandler(self.fn, encoding="utf-8", maxBytes=1)
@@ -5284,6 +5291,14 @@ def rotator(source, dest):
         rh.close()
 
 class TimedRotatingFileHandlerTest(BaseFileTest):
+    def test_should_not_rollover(self):
+        # See bpo-45401. Should only ever rollover regular files
+        fh = logging.handlers.TimedRotatingFileHandler(
+                os.devnull, 'S', encoding="utf-8", backupCount=1)
+        time.sleep(1.1)    # a little over a second ...
+        r = logging.makeLogRecord({'msg': 'testing - device file'})
+        self.assertFalse(fh.shouldRollover(r))
+
     # other test methods added below
     def test_rollover(self):
         fh = logging.handlers.TimedRotatingFileHandler(