diff -r d86eabe2c457 Lib/selectors.py
--- a/Lib/selectors.py	Mon Aug 08 03:11:06 2016 +0300
+++ b/Lib/selectors.py	Sun Aug 14 10:20:54 2016 +0200
@@ -408,8 +408,13 @@ if hasattr(select, 'epoll'):
                 epoll_events |= select.EPOLLIN
             if events & EVENT_WRITE:
                 epoll_events |= select.EPOLLOUT
-            self._epoll.register(key.fd, epoll_events)
-            return key
+            try:
+                self._epoll.register(key.fd, epoll_events)
+            except BaseException:
+                super().unregister(fileobj)
+                raise
+            else:
+                return key
 
         def unregister(self, fileobj):
             key = super().unregister(fileobj)
@@ -530,15 +535,20 @@ if hasattr(select, 'kqueue'):
 
         def register(self, fileobj, events, data=None):
             key = super().register(fileobj, events, data)
-            if events & EVENT_READ:
-                kev = select.kevent(key.fd, select.KQ_FILTER_READ,
-                                    select.KQ_EV_ADD)
-                self._kqueue.control([kev], 0, 0)
-            if events & EVENT_WRITE:
-                kev = select.kevent(key.fd, select.KQ_FILTER_WRITE,
-                                    select.KQ_EV_ADD)
-                self._kqueue.control([kev], 0, 0)
-            return key
+            try:
+                if events & EVENT_READ:
+                    kev = select.kevent(key.fd, select.KQ_FILTER_READ,
+                                        select.KQ_EV_ADD)
+                    self._kqueue.control([kev], 0, 0)
+                if events & EVENT_WRITE:
+                    kev = select.kevent(key.fd, select.KQ_FILTER_WRITE,
+                                        select.KQ_EV_ADD)
+                    self._kqueue.control([kev], 0, 0)
+            except BaseException:
+                super().unregister(fileobj)
+                raise
+            else:
+                return key
 
         def unregister(self, fileobj):
             key = super().unregister(fileobj)
diff -r d86eabe2c457 Lib/test/test_selectors.py
--- a/Lib/test/test_selectors.py	Mon Aug 08 03:11:06 2016 +0300
+++ b/Lib/test/test_selectors.py	Sun Aug 14 10:20:54 2016 +0200
@@ -9,6 +9,7 @@ from test import support
 from time import sleep
 import unittest
 import unittest.mock
+import tempfile
 from time import monotonic as time
 try:
     import resource
@@ -475,6 +476,16 @@ class EpollSelectorTestCase(BaseSelector
 
     SELECTOR = getattr(selectors, 'EpollSelector', None)
 
+    def test_register_file(self):
+        # epoll(7) returns EPERM when given a file to watch
+        s = self.SELECTOR()
+        with tempfile.NamedTemporaryFile() as f:
+            with self.assertRaises(IOError):
+                s.register(f, selectors.EVENT_READ)
+            # the SelectorKey has been removed
+            with self.assertRaises(KeyError):
+                s.get_key(f)
+
 
 @unittest.skipUnless(hasattr(selectors, 'KqueueSelector'),
                      "Test needs selectors.KqueueSelector)")
@@ -482,6 +493,20 @@ class KqueueSelectorTestCase(BaseSelecto
 
     SELECTOR = getattr(selectors, 'KqueueSelector', None)
 
+    def test_register_bad_fd(self):
+        # a file descriptor that's been closed should raise an OSError
+        # with EBADF
+        s = self.SELECTOR()
+        pipe_read, pipe_write = os.pipe()
+        os.close(pipe_read)
+        os.close(pipe_write)
+        with self.assertRaises(OSError) as cm:
+            s.register(pipe_read, selectors.EVENT_READ)
+        self.assertEqual(cm.exception.errno, errno.EBADF)
+        # the SelectorKey has been removed
+        with self.assertRaises(KeyError):
+            s.get_key(pipe_read)
+
 
 @unittest.skipUnless(hasattr(selectors, 'DevpollSelector'),
                      "Test needs selectors.DevpollSelector")