diff --git a/Lib/test/test_posix.py b/Lib/test/test_posix.py
index 6b4272f..24e5b1c 100644
--- a/Lib/test/test_posix.py
+++ b/Lib/test/test_posix.py
@@ -150,6 +150,10 @@
         if hasattr(posix, 'utime'):
             now = time.time()
             posix.utime(test_support.TESTFN, None)
+            self.assertRaises(TypeError, posix.utime, test_support.TESTFN, (None, None))
+            self.assertRaises(TypeError, posix.utime, test_support.TESTFN, (now, None))
+            self.assertRaises(TypeError, posix.utime, test_support.TESTFN, (None, now))
+            posix.utime(test_support.TESTFN, (int(now), int(now)))
             posix.utime(test_support.TESTFN, (now, now))
 
 def test_main():