diff --git a/Lib/test/test_memoryview.py b/Lib/test/test_memoryview.py
index dca48b1..0f6fc55 100644
--- a/Lib/test/test_memoryview.py
+++ b/Lib/test/test_memoryview.py
@@ -6,6 +6,8 @@
 import unittest
 import test.support
 import sys
+import gc
+import weakref
 
 
 class CommonMemoryTests:
@@ -157,6 +159,36 @@
         m = self.check_attributes_with_type(bytearray)
         self.assertEquals(m.readonly, False)
 
+    def test_getbuffer(self):
+        # Test PyObject_GetBuffer() on a memoryview object.
+        b = self.base_object
+        oldrefcount = sys.getrefcount(b)
+        m = self._view(b)
+        oldviewrefcount = sys.getrefcount(m)
+        s = str(m, "utf-8")
+        self._check_contents(b, s.encode("utf-8"))
+        self.assertEquals(sys.getrefcount(m), oldviewrefcount)
+        m = None
+        self.assertEquals(sys.getrefcount(b), oldrefcount)
+
+    def test_gc(self):
+        class MyBytes(bytes):
+            pass
+        class MyObject:
+            pass
+
+        # Create a reference cycle through a memoryview object
+        b = MyBytes(b'abc')
+        m = self._view(b)
+        o = MyObject()
+        b.m = m
+        b.o = o
+        wr = weakref.ref(o)
+        b = m = o = None
+        # The cycle must be broken
+        gc.collect()
+        self.assert_(wr() is None, wr())
+
 
 class MemoryviewTest(unittest.TestCase, CommonMemoryTests):
 
diff --git a/Misc/NEWS b/Misc/NEWS
index 78a89ec..2f1f58a 100644
--- a/Misc/NEWS
+++ b/Misc/NEWS
@@ -12,6 +12,9 @@
 Core and Builtins
 -----------------
 
+- Issue #3712: The memoryview object had a reference leak and didn't support
+  cyclic garbage collection.
+
 - Issue #3668: Fix a memory leak with the "s*" argument parser in
   PyArg_ParseTuple and friends, which occurred when the argument for "s*" 
   was correctly parsed but parsing of subsequent arguments failed.
diff --git a/Objects/memoryobject.c b/Objects/memoryobject.c
index bd5820f..fbb1af6 100644
--- a/Objects/memoryobject.c
+++ b/Objects/memoryobject.c
@@ -3,24 +3,34 @@
 
 #include "Python.h"
 
+static void
+dup_buffer(Py_buffer *dest, Py_buffer *src)
+{
+	*dest = *src;
+        if (src->shape == &(src->len))
+            dest->shape = &(dest->len);
+        if (src->strides == &(src->itemsize))
+            dest->strides = &(dest->itemsize);
+}
+
 static int
 memory_getbuf(PyMemoryViewObject *self, Py_buffer *view, int flags)
 {
-        if (view != NULL) {
-		if (self->view.obj)
-			Py_INCREF(self->view.obj);
-		*view = self->view;
-	}
-	if (self->view.obj == NULL)
-		return 0;
-        return self->view.obj->ob_type->tp_as_buffer->bf_getbuffer(
-            self->view.obj, NULL, PyBUF_FULL);
+	int res = 0;
+	/* XXX for whatever reason fixing the flags seems necessary */
+	if (self->view.readonly)
+		flags &= ~PyBUF_WRITABLE;
+	if (self->view.obj != NULL)
+		res = PyObject_GetBuffer(self->view.obj, view, flags);
+	if (view)
+		dup_buffer(view, &self->view);
+	return res;
 }
 
 static void
 memory_releasebuf(PyMemoryViewObject *self, Py_buffer *view)
 {
-	PyBuffer_Release(&self->view);
+	PyBuffer_Release(view);
 }
 
 PyDoc_STRVAR(memory_doc,
@@ -33,18 +43,15 @@
 {
 	PyMemoryViewObject *mview;
 
-	mview = (PyMemoryViewObject *)PyObject_New(PyMemoryViewObject,
-						   &PyMemoryView_Type);
-	if (mview == NULL) return NULL;
+	mview = (PyMemoryViewObject *)
+		PyObject_GC_New(PyMemoryViewObject, &PyMemoryView_Type);
+	if (mview == NULL)
+		return NULL;
 	mview->base = NULL;
-        /* XXX there should be an API to duplicate a buffer object */
-	mview->view = *info;
-        if (info->shape == &(info->len))
-            mview->view.shape = &(mview->view.len);
-        if (info->strides == &(info->itemsize))
-            mview->view.strides = &(mview->view.itemsize);
+	dup_buffer(&mview->view, info);
         /* NOTE: mview->view.obj should already have been incref'ed as
            part of PyBuffer_FillInfo(). */
+	_PyObject_GC_TRACK(mview);
 	return (PyObject *)mview;
 }
 
@@ -60,9 +67,10 @@
                 return NULL;
         }
 
-        mview = (PyMemoryViewObject *)PyObject_New(PyMemoryViewObject,
-                                                   &PyMemoryView_Type);
-        if (mview == NULL) return NULL;
+	mview = (PyMemoryViewObject *)
+		PyObject_GC_New(PyMemoryViewObject, &PyMemoryView_Type);
+        if (mview == NULL)
+		return NULL;
 
         mview->base = NULL;
         if (PyObject_GetBuffer(base, &(mview->view), PyBUF_FULL_RO) < 0) {
@@ -72,6 +80,7 @@
 
         mview->base = base;
         Py_INCREF(base);
+	_PyObject_GC_TRACK(mview);
         return (PyObject *)mview;
 }
 
@@ -233,8 +242,9 @@
                 return NULL;
         }
 
-        mem = PyObject_New(PyMemoryViewObject, &PyMemoryView_Type);
-        if (mem == NULL) return NULL;
+        mem = PyObject_GC_New(PyMemoryViewObject, &PyMemoryView_Type);
+        if (mem == NULL)
+		return NULL;
 
         view = &mem->view;
         flags = PyBUF_FULL_RO;
@@ -245,7 +255,7 @@
         }
 
         if (PyObject_GetBuffer(obj, view, flags) != 0) {
-                PyObject_DEL(mem);
+                Py_DECREF(mem);
                 return NULL;
         }
 
@@ -253,11 +263,12 @@
                 /* no copy needed */
                 Py_INCREF(obj);
                 mem->base = obj;
+		_PyObject_GC_TRACK(mem);
                 return (PyObject *)mem;
         }
         /* otherwise a copy is needed */
         if (buffertype == PyBUF_WRITE) {
-                PyObject_DEL(mem);
+                Py_DECREF(mem);
                 PyErr_SetString(PyExc_BufferError,
                                 "writable contiguous buffer requested "
                                 "for a non-contiguousobject.");
@@ -265,7 +276,7 @@
         }
         bytes = PyBytes_FromStringAndSize(NULL, view->len);
         if (bytes == NULL) {
-                PyBuffer_Release(view);
+                Py_DECREF(mem);
                 return NULL;
         }
         dest = PyBytes_AS_STRING(bytes);
@@ -280,7 +291,7 @@
         else {
                 if (_indirect_copy_nd(dest, view, fort) < 0) {
                         Py_DECREF(bytes);
-                        PyBuffer_Release(view);
+			Py_DECREF(mem);
                         return NULL;
                 }
         }
@@ -290,15 +301,16 @@
                 mem->base = PyTuple_Pack(2, obj, bytes);
                 Py_DECREF(bytes);
 		if (mem->base == NULL) {
-			PyBuffer_Release(view);
+			Py_DECREF(mem);
 			return NULL;
 		}
         }
         else {
-                PyBuffer_Release(view);
+                PyBuffer_Release(view);  /* XXX ? */
                 /* steal the reference */
                 mem->base = bytes;
         }
+	_PyObject_GC_TRACK(mem);
         return (PyObject *)mem;
 }
 
@@ -444,6 +456,7 @@
 static void
 memory_dealloc(PyMemoryViewObject *self)
 {
+	_PyObject_GC_UNTRACK(self);
         if (self->view.obj != NULL) {
             if (self->base && PyTuple_Check(self->base)) {
                 /* Special case when first element is generic object
@@ -468,7 +481,7 @@
             }
             Py_CLEAR(self->base);
         }
-        PyObject_DEL(self);
+	PyObject_GC_Del(self);
 }
 
 static PyObject *
@@ -749,6 +762,25 @@
 }
 
 
+static int
+memory_traverse(PyMemoryViewObject *self, visitproc visit, void *arg)
+{
+	if (self->base != NULL)
+		Py_VISIT(self->base);
+	if (self->view.obj != NULL)
+		Py_VISIT(self->view.obj);
+	return 0;
+}
+
+static int
+memory_clear(PyMemoryViewObject *self)
+{
+	Py_CLEAR(self->base);
+	PyBuffer_Release(&self->view);
+	return 0;
+}
+
+
 /* As mapping */
 static PyMappingMethods memory_as_mapping = {
 	(lenfunc)memory_length, /*mp_length*/
@@ -785,10 +817,10 @@
 	PyObject_GenericGetAttr,		/* tp_getattro */
 	0,					/* tp_setattro */
 	&memory_as_buffer,			/* tp_as_buffer */
-	Py_TPFLAGS_DEFAULT,			/* tp_flags */
+	Py_TPFLAGS_DEFAULT | Py_TPFLAGS_HAVE_GC,/* tp_flags */
 	memory_doc,				/* tp_doc */
-	0,					/* tp_traverse */
-	0,					/* tp_clear */
+	(traverseproc)memory_traverse,		/* tp_traverse */
+	(inquiry)memory_clear,			/* tp_clear */
 	memory_richcompare,                     /* tp_richcompare */
 	0,					/* tp_weaklistoffset */
 	0,					/* tp_iter */