diff --git a/Lib/test/test_os/test_os.py b/Lib/test/test_os/test_os.py
index 6be86ac56a0d1f..f9919e824b1abe 100644
--- a/Lib/test/test_os/test_os.py
+++ b/Lib/test/test_os/test_os.py
@@ -1058,11 +1058,18 @@ def support_subsecond(self, filename):
                 or (st.st_mtime != st[8])
                 or (st.st_ctime != st[9]))
 
+    def support_atime(self, filename):
+        # Heuristic to check if the filesystem stores the access time.
+        # Use whole seconds, to not depend on the timestamp resolution.
+        os.utime(filename, (1, 2))
+        return os.stat(filename).st_atime == 1
+
     def _test_utime(self, set_time, filename=None):
         if not filename:
             filename = self.fname
 
         support_subsecond = self.support_subsecond(filename)
+        support_atime = self.support_atime(filename)
         if support_subsecond:
             # Timestamp with a resolution of 1 microsecond (10^-6).
             #
@@ -1089,18 +1096,22 @@ def _test_utime(self, set_time, filename=None):
             # digits worth of sub-second precision.
             # Some day it would be good to fix this upstream.
             delta=1e-5
-            self.assertAlmostEqual(st.st_atime, atime_ns * 1e-9, delta=1e-5)
+            if support_atime:
+                self.assertAlmostEqual(st.st_atime, atime_ns * 1e-9, delta=1e-5)
+                self.assertAlmostEqual(st.st_atime_ns, atime_ns, delta=1e9 * 1e-5)
             self.assertAlmostEqual(st.st_mtime, mtime_ns * 1e-9, delta=1e-5)
-            self.assertAlmostEqual(st.st_atime_ns, atime_ns, delta=1e9 * 1e-5)
             self.assertAlmostEqual(st.st_mtime_ns, mtime_ns, delta=1e9 * 1e-5)
         else:
             if support_subsecond:
-                self.assertAlmostEqual(st.st_atime, atime_ns * 1e-9, delta=1e-6)
+                if support_atime:
+                    self.assertAlmostEqual(st.st_atime, atime_ns * 1e-9, delta=1e-6)
                 self.assertAlmostEqual(st.st_mtime, mtime_ns * 1e-9, delta=1e-6)
             else:
-                self.assertEqual(st.st_atime, atime_ns * 1e-9)
+                if support_atime:
+                    self.assertEqual(st.st_atime, atime_ns * 1e-9)
                 self.assertEqual(st.st_mtime, mtime_ns * 1e-9)
-            self.assertEqual(st.st_atime_ns, atime_ns)
+            if support_atime:
+                self.assertEqual(st.st_atime_ns, atime_ns)
             self.assertEqual(st.st_mtime_ns, mtime_ns)
 
     def test_utime(self):