diff --git a/Lib/test/eintrdata/eintr_tester.py b/Lib/test/eintrdata/eintr_tester.py
index e3f1aa519e..81b6277a04 100644
--- a/Lib/test/eintrdata/eintr_tester.py
+++ b/Lib/test/eintrdata/eintr_tester.py
@@ -424,6 +424,8 @@ class SelectEINTRTest(EINTRBaseTest):
         self.stop_alarm()
         self.assertGreaterEqual(dt, self.sleep_time)
 
+    @unittest.skipIf(sys.platform == "darwin",
+                     "poll may fail on macOS; see issue #28087")
     @unittest.skipUnless(hasattr(select, 'poll'), 'need select.poll')
     def test_poll(self):
         poller = select.poll()
diff --git a/Lib/test/test_asyncore.py b/Lib/test/test_asyncore.py
index 38579168cf..18f1ea23fa 100644
--- a/Lib/test/test_asyncore.py
+++ b/Lib/test/test_asyncore.py
@@ -656,6 +656,9 @@ class BaseTestAPI:
         if HAS_UNIX_SOCKETS and self.family == socket.AF_UNIX:
             self.skipTest("Not applicable to AF_UNIX sockets.")
 
+        if sys.platform == "darwin" and self.use_poll:
+            self.skipTest("poll may fail on macOS; see issue #28087")
+
         class TestClient(BaseClient):
             def handle_expt(self):
                 self.socket.recv(1024, socket.MSG_OOB)
diff --git a/Misc/NEWS b/Misc/NEWS
index c428d77f17..c7d273c241 100644
--- a/Misc/NEWS
+++ b/Misc/NEWS
@@ -201,6 +201,10 @@ Build
 Tests
 -----
 
+- bpo-28087: Skip test_asyncore and test_eintr poll failures on macOS.
+  Skip some tests of select.poll when running on macOS due to unresolved
+  issues with the underlying system poll function on some macOS versions.
+
 - bpo-30197: Enhanced functions swap_attr() and swap_item() in the
   test.support module.  They now work when delete replaced attribute or item
   inside the with statement.  The old value of the attribute or item (or None