diff --git a/Doc/library/select.rst b/Doc/library/select.rst
index 4fafb117b8d..5494eef1732 100644
--- a/Doc/library/select.rst
+++ b/Doc/library/select.rst
@@ -391,6 +391,9 @@ linearly scanned again. :c:func:`select` is O(highest file descriptor), while
    +-------------------+------------------------------------------+
    | :const:`POLLHUP`  | Hung up                                  |
    +-------------------+------------------------------------------+
+   | :const:`POLLRDHUP`| Stream socket peer closed connection, or |
+   |                   | shut down writing half of connection     |
+   +-------------------+------------------------------------------+
    | :const:`POLLNVAL` | Invalid request: descriptor not open     |
    +-------------------+------------------------------------------+
 
diff --git a/Misc/NEWS b/Misc/NEWS
index 803bef0563d..16d447659fc 100644
--- a/Misc/NEWS
+++ b/Misc/NEWS
@@ -28,7 +28,8 @@ Library
 
 - Expose the EPOLLEXCLUSIVE constant (when it is defined) in the select module.
 
-- Issue #27567: Expose the EPOLLRDHUP constant in the select module.
+- Issue #27567: Expose the EPOLLRDHUP and POLLRDHUP constants in the select
+  module.
 
 - Issue #1621: Avoid signed int negation overflow in the "audioop" module.
 
diff --git a/Modules/selectmodule.c b/Modules/selectmodule.c
index c84c3cc26b5..0f90ce259aa 100644
--- a/Modules/selectmodule.c
+++ b/Modules/selectmodule.c
@@ -4,6 +4,10 @@
    have any value except INVALID_SOCKET.
 */
 
+#if defined(HAVE_POLL_H) && !defined(_GNU_SOURCE)
+#define _GNU_SOURCE
+#endif
+
 #include "Python.h"
 #include <structmember.h>
 
@@ -2451,6 +2455,10 @@ PyInit_select(void)
 #endif
 #ifdef POLLMSG
         PyModule_AddIntMacro(m, POLLMSG);
+#endif
+#ifdef POLLRDHUP
+        /* Kernel 2.6.17+ */
+        PyModule_AddIntMacro(m, POLLRDHUP);
 #endif
     }
 #endif /* HAVE_POLL */