diff --git a/Lib/asyncio/tasks.py b/Lib/asyncio/tasks.py
index 2bee5c050ded7d..faee0cec6b668d 100644
--- a/Lib/asyncio/tasks.py
+++ b/Lib/asyncio/tasks.py
@@ -109,6 +109,7 @@ def __init__(self, coro, *, loop=None, name=None):
         self._fut_waiter = None
         self._coro = coro
         self._context = contextvars.copy_context()
+        self.__cancel_requested__ = False
 
         self._loop.call_soon(self.__step, context=self._context)
         _register_task(self)
@@ -201,6 +202,10 @@ def cancel(self, msg=None):
         self._log_traceback = False
         if self.done():
             return False
+        if self.__cancel_requested__:
+            # Cancel was requested by previous task.cancel() call
+            return False
+        self.__cancel_requested__ = True
         if self._fut_waiter is not None:
             if self._fut_waiter.cancel(msg=msg):
                 # Leave self._fut_waiter; it may be a Task that
@@ -634,7 +639,7 @@ def _ensure_future(coro_or_future, *, loop=None):
         loop = events._get_event_loop(stacklevel=4)
     try:
         return loop.create_task(coro_or_future)
-    except RuntimeError: 
+    except RuntimeError:
         if not called_wrap_awaitable:
             coro_or_future.close()
         raise
diff --git a/Lib/test/test_asyncio/test_tasks.py b/Lib/test/test_asyncio/test_tasks.py
index 8c4dceacdeec96..b14240327d60c7 100644
--- a/Lib/test/test_asyncio/test_tasks.py
+++ b/Lib/test/test_asyncio/test_tasks.py
@@ -496,6 +496,25 @@ async def run():
         # This also distinguishes from the initial has_cycle=None.
         self.assertEqual(has_cycle, False)
 
+    def test___cancel_requested__(self):
+        loop = asyncio.new_event_loop()
+
+        async def task():
+            await asyncio.sleep(10)
+            return 12
+
+        try:
+            t = self.new_task(loop, task())
+            self.assertFalse(t.__cancel_requested__)
+            self.assertTrue(t.cancel())
+            self.assertTrue(t.__cancel_requested__)
+            self.assertFalse(t.cancel())
+
+            with self.assertRaises(asyncio.CancelledError):
+                loop.run_until_complete(t)
+        finally:
+            loop.close()
+
     def test_cancel(self):
 
         def gen():
diff --git a/Modules/_asynciomodule.c b/Modules/_asynciomodule.c
index 72dbdb8902f121..ef176b6bc596a9 100644
--- a/Modules/_asynciomodule.c
+++ b/Modules/_asynciomodule.c
@@ -91,6 +91,7 @@ typedef struct {
     PyObject *task_context;
     int task_must_cancel;
     int task_log_destroy_pending;
+    int task_cancel_requested;
 } TaskObj;
 
 typedef struct {
@@ -2039,6 +2040,7 @@ _asyncio_Task___init___impl(TaskObj *self, PyObject *coro, PyObject *loop,
     Py_CLEAR(self->task_fut_waiter);
     self->task_must_cancel = 0;
     self->task_log_destroy_pending = 1;
+    self->task_cancel_requested = 0;
     Py_INCREF(coro);
     Py_XSETREF(self->task_coro, coro);
 
@@ -2141,6 +2143,32 @@ TaskObj_get_fut_waiter(TaskObj *task, void *Py_UNUSED(ignored))
     Py_RETURN_NONE;
 }
 
+static PyObject *
+TaskObj_get_cancel_requested(TaskObj *task, void *Py_UNUSED(ignored))
+{
+    if (task->task_cancel_requested) {
+        Py_RETURN_TRUE;
+    }
+    else {
+        Py_RETURN_FALSE;
+    }
+}
+
+static int
+TaskObj_set_cancel_requested(TaskObj *task, PyObject *val, void *Py_UNUSED(ignored))
+{
+    if (val == NULL) {
+        PyErr_SetString(PyExc_AttributeError, "cannot delete attribute");
+        return -1;
+    }
+    int is_true = PyObject_IsTrue(val);
+    if (is_true < 0) {
+        return -1;
+    }
+    task->task_cancel_requested = is_true;
+    return 0;
+}
+
 /*[clinic input]
 _asyncio.Task._make_cancelled_error
 
@@ -2205,6 +2233,11 @@ _asyncio_Task_cancel_impl(TaskObj *self, PyObject *msg)
         Py_RETURN_FALSE;
     }
 
+    if (self->task_cancel_requested) {
+        Py_RETURN_FALSE;
+    }
+    self->task_cancel_requested = 1;
+
     if (self->task_fut_waiter) {
         PyObject *res;
         int is_true;
@@ -2473,6 +2506,8 @@ static PyGetSetDef TaskType_getsetlist[] = {
     {"_must_cancel", (getter)TaskObj_get_must_cancel, NULL, NULL},
     {"_coro", (getter)TaskObj_get_coro, NULL, NULL},
     {"_fut_waiter", (getter)TaskObj_get_fut_waiter, NULL, NULL},
+    {"__cancel_requested__", (getter)TaskObj_get_cancel_requested,
+                             (setter)TaskObj_set_cancel_requested, NULL},
     {NULL} /* Sentinel */
 };