diff --git a/Lib/selectors.py b/Lib/selectors.py
index bb15a1cb1b..c3b065b522 100644
--- a/Lib/selectors.py
+++ b/Lib/selectors.py
@@ -50,12 +50,11 @@ SelectorKey.__doc__ = """SelectorKey(fileobj, fd, events, data)
     Object used to associate a file object to its backing
     file descriptor, selected event mask, and attached data.
 """
-if sys.version_info >= (3, 5):
-    SelectorKey.fileobj.__doc__ = 'File object registered.'
-    SelectorKey.fd.__doc__ = 'Underlying file descriptor.'
-    SelectorKey.events.__doc__ = 'Events that must be waited for on this file object.'
-    SelectorKey.data.__doc__ = ('''Optional opaque data associated to this file object.
-    For example, this could be used to store a per-client session ID.''')
+SelectorKey.fileobj.__doc__ = 'File object registered.'
+SelectorKey.fd.__doc__ = 'Underlying file descriptor.'
+SelectorKey.events.__doc__ = 'Events that must be waited for on this file object.'
+SelectorKey.data.__doc__ = ('''Optional opaque data associated to this file object.
+For example, this could be used to store a per-client session ID.''')
 
 
 class _SelectorMapping(Mapping):
@@ -510,6 +509,7 @@ if hasattr(select, 'kqueue'):
         def __init__(self):
             super().__init__()
             self._selector = select.kqueue()
+            self._max_events = 0
 
         def fileno(self):
             return self._selector.fileno()
@@ -521,10 +521,12 @@ if hasattr(select, 'kqueue'):
                     kev = select.kevent(key.fd, select.KQ_FILTER_READ,
                                         select.KQ_EV_ADD)
                     self._selector.control([kev], 0, 0)
+                    self._max_events += 1
                 if events & EVENT_WRITE:
                     kev = select.kevent(key.fd, select.KQ_FILTER_WRITE,
                                         select.KQ_EV_ADD)
                     self._selector.control([kev], 0, 0)
+                    self._max_events += 1
             except:
                 super().unregister(fileobj)
                 raise
@@ -535,6 +537,7 @@ if hasattr(select, 'kqueue'):
             if key.events & EVENT_READ:
                 kev = select.kevent(key.fd, select.KQ_FILTER_READ,
                                     select.KQ_EV_DELETE)
+                self._max_events -= 1
                 try:
                     self._selector.control([kev], 0, 0)
                 except OSError:
@@ -544,6 +547,7 @@ if hasattr(select, 'kqueue'):
             if key.events & EVENT_WRITE:
                 kev = select.kevent(key.fd, select.KQ_FILTER_WRITE,
                                     select.KQ_EV_DELETE)
+                self._max_events -= 1
                 try:
                     self._selector.control([kev], 0, 0)
                 except OSError:
@@ -556,7 +560,7 @@ if hasattr(select, 'kqueue'):
             # If max_ev is 0, kqueue will ignore the timeout. For consistent
             # behavior with the other selector classes, we prevent that here
             # (using max). See https://bugs.python.org/issue29255
-            max_ev = max(len(self._fd_to_key), 1)
+            max_ev = self._max_events or 1
             ready = []
             try:
                 kev_list = self._selector.control(None, max_ev, timeout)
diff --git a/Lib/test/test_selectors.py b/Lib/test/test_selectors.py
index 42c5e8879b..af730a8dec 100644
--- a/Lib/test/test_selectors.py
+++ b/Lib/test/test_selectors.py
@@ -19,6 +19,10 @@ except ImportError:
     resource = None
 
 
+if support.is_emscripten or support.is_wasi:
+    raise unittest.SkipTest("Cannot create socketpair on Emscripten/WASI.")
+
+
 if hasattr(socket, 'socketpair'):
     socketpair = socket.socketpair
 else:
@@ -276,6 +280,35 @@ class BaseSelectorTestCase:
 
         self.assertEqual([(wr_key, selectors.EVENT_WRITE)], result)
 
+    def test_select_read_write(self):
+        # gh-110038: when a file descriptor is registered for both read and
+        # write, the two events must be seen on a single call to select().
+        s = self.SELECTOR()
+        self.addCleanup(s.close)
+
+        sock1, sock2 = self.make_socketpair()
+        sock2.send(b"foo")
+        my_key = s.register(sock1, selectors.EVENT_READ | selectors.EVENT_WRITE)
+
+        seen_read, seen_write = False, False
+        result = s.select()
+        # We get the read and write either in the same result entry or in two
+        # distinct entries with the same key.
+        self.assertLessEqual(len(result), 2)
+        for key, events in result:
+            self.assertTrue(isinstance(key, selectors.SelectorKey))
+            self.assertEqual(key, my_key)
+            self.assertFalse(events & ~(selectors.EVENT_READ |
+                                        selectors.EVENT_WRITE))
+            if events & selectors.EVENT_READ:
+                self.assertFalse(seen_read)
+                seen_read = True
+            if events & selectors.EVENT_WRITE:
+                self.assertFalse(seen_write)
+                seen_write = True
+        self.assertTrue(seen_read)
+        self.assertTrue(seen_write)
+
     def test_context_manager(self):
         s = self.SELECTOR()
         self.addCleanup(s.close)
@@ -446,6 +479,7 @@ class ScalableSelectorMixIn:
     # see issue #18963 for why it's skipped on older OS X versions
     @support.requires_mac_ver(10, 5)
     @unittest.skipUnless(resource, "Test needs resource module")
+    @support.requires_resource('cpu')
     def test_above_fd_setsize(self):
         # A scalable implementation should have no problem with more than
         # FD_SETSIZE file descriptors. Since we don't know the value, we just