diff -r 26f6d8cc2749 Modules/selectmodule.c
--- a/Modules/selectmodule.c	Thu Jan 28 15:44:10 2016 +0100
+++ b/Modules/selectmodule.c	Thu Jan 28 16:47:57 2016 +0100
@@ -1220,6 +1220,11 @@ static int select_have_broken_poll(void)
 typedef struct {
     PyObject_HEAD
     SOCKET epfd;                        /* epoll control file descriptor */
+
+    /* Buffer used by pyepoll_poll() to avoid calling
+     * PyMem_Malloc()/PyMem_Free() for each time poll. */
+    Py_ssize_t allocated;
+    struct epoll_event *buffer;
 } pyEpoll_Object;
 
 static PyTypeObject pyEpoll_Type;
@@ -1236,6 +1241,11 @@ static int
 pyepoll_internal_close(pyEpoll_Object *self)
 {
     int save_errno = 0;
+    if (self->buffer) {
+        PyMem_Free(self->buffer);
+        self->allocated = 0;
+        self->buffer = NULL;
+    }
     if (self->epfd >= 0) {
         int epfd = self->epfd;
         self->epfd = -1;
@@ -1284,6 +1294,9 @@ newPyEpoll_Object(PyTypeObject *type, in
     }
 #endif
 
+    self->allocated = 0;
+    self->buffer = NULL;
+
     return (PyObject *)self;
 }
 
@@ -1492,6 +1505,8 @@ pyepoll_poll(pyEpoll_Object *self, PyObj
     PyObject *elist = NULL, *etuple = NULL;
     struct epoll_event *evs = NULL;
     _PyTime_t timeout, ms, deadline;
+    Py_ssize_t allocated;
+    struct epoll_event *buffer;
 
     if (self->epfd < 0)
         return pyepoll_err_closed();
@@ -1536,13 +1551,39 @@ pyepoll_poll(pyEpoll_Object *self, PyObj
                      maxevents);
         return NULL;
     }
-
-    evs = PyMem_New(struct epoll_event, maxevents);
-    if (evs == NULL) {
+    if (maxevents > PY_SSIZE_T_MAX / (Py_ssize_t)sizeof(struct epoll_event)) {
         PyErr_NoMemory();
         return NULL;
     }
 
+    /* steal the buffer (the GIL ensures that the exchange is atomic) */
+    allocated = self->allocated;
+    buffer = self->buffer;
+    self->allocated = 0;
+    self->buffer = NULL;
+
+    if (allocated < maxevents) {
+        Py_ssize_t size;
+
+        size = maxevents;
+        if (allocated && size < PY_SSIZE_T_MAX - maxevents / 2) {
+            /* if resize, overallocate by 50% */
+            size += maxevents / 2;
+        }
+
+        size *= sizeof(struct epoll_event);
+        evs = (struct epoll_event *)PyMem_Realloc(buffer, size);
+        if (evs == NULL) {
+            PyErr_NoMemory();
+            goto error;
+        }
+        allocated = maxevents;
+        buffer = evs;
+    }
+    else {
+        evs = buffer;
+    }
+
     do {
         Py_BEGIN_ALLOW_THREADS
         errno = 0;
@@ -1586,8 +1627,19 @@ pyepoll_poll(pyEpoll_Object *self, PyObj
         PyList_SET_ITEM(elist, i, etuple);
     }
 
-    error:
-    PyMem_Free(evs);
+error:
+    /* always keep the largest buffer */
+    if (self->allocated < allocated) {
+        /* if another thread allocated a smaller buffer, release it */
+        PyMem_Free(self->buffer);
+        self->allocated = allocated;
+        self->buffer = buffer;
+    }
+    else {
+        /* another thread allocated a larger buffer,
+         * release the small buffer */
+        PyMem_Free(buffer);
+    }
     return elist;
 }