diff --git a/Objects/iterobject.c b/Objects/iterobject.c
index 65af18a..6961fc3 100644
--- a/Objects/iterobject.c
+++ b/Objects/iterobject.c
@@ -316,7 +316,52 @@ anextawaitable_traverse(anextawaitableobject *obj, visitproc visit, void *arg)
 static PyObject *
 anextawaitable_iternext(anextawaitableobject *obj)
 {
-    PyObject *result = PyIter_Next(obj->wrapped);
+    /* Consider the following class:
+     *
+     *     class A:
+     *         async def __anext__(self):
+     *             ...
+     *     a = A()
+     *
+     * Then `await anext(a)` should call
+     * a.__anext__().__await__().__next__()
+     *
+     * On the other hand, given
+     *
+     *     async def agen():
+     *         yield 1
+     *         yield 2
+     *     gen = agen()
+     *
+     * Then `await anext(gen)` can just call
+     * gen.__anext__().__next__()
+     */
+    assert(obj->wrapped != NULL);
+    PyObject *awaitable = _PyCoro_GetAwaitableIter(obj->wrapped);
+    if (awaitable == NULL) {
+        return NULL;
+    }
+    if (Py_TYPE(awaitable)->tp_iternext == NULL) {
+        /* _PyCoro_GetAwaitableIter returns a Coroutine, a Generator,
+         * or an iterator. Of these, only coroutines lack tp_iternext.
+         */
+        assert(PyCoro_CheckExact(awaitable));
+        unaryfunc getter = Py_TYPE(awaitable)->tp_as_async->am_await;
+        PyObject *new_awaitable = getter(awaitable);
+        if (new_awaitable == NULL) {
+            Py_DECREF(awaitable);
+            return NULL;
+        }
+        Py_SETREF(awaitable, new_awaitable);
+        if (Py_TYPE(awaitable)->tp_iternext == NULL) {
+            PyErr_SetString(PyExc_TypeError,
+                            "__await__ returned a non-iterable");
+            Py_DECREF(awaitable);
+            return NULL;
+        }
+    }
+    PyObject *result = (*Py_TYPE(awaitable)->tp_iternext)(awaitable);
+    Py_DECREF(awaitable);
     if (result != NULL) {
         return result;
     }