diff --git a/imperative/python/megengine/autodiff/grad_manager.py b/imperative/python/megengine/autodiff/grad_manager.py
index 47456fa674fdfd5a30d7d258f1a70aee04212459..19652fa30611f09c76d1e455101263aabc3de1e5 100644
--- a/imperative/python/megengine/autodiff/grad_manager.py
+++ b/imperative/python/megengine/autodiff/grad_manager.py
@@ -345,12 +345,12 @@ class GradManager:
     def __exit__(self, exc_type, exc_val, exc_tb):
         self.release()
 
-    def __and__(self, other):
+    def __or__(self, other):
         if isinstance(other, GradManager):
             return GradManagerGroup([self, other])
         return NotImplemented
 
-    __rand__ = __and__
+    __ror__ = __or__
 
 
 class GradManagerGroup:
@@ -364,8 +364,6 @@ class GradManagerGroup:
             return NotImplemented
         return GradManagerGroup([*self._gms, *other._gms])
 
-    __and__ = merge_with
-    __rand__ = merge_with
     __or__ = merge_with
     __ror__ = merge_with
 
diff --git a/imperative/python/src/grad.cpp b/imperative/python/src/grad.cpp
index 23507848952b811daffc8ac3d844f295c10b32f9..e47f733d8bcaa09f7a7de0e2baad6631465c47f6 100644
--- a/imperative/python/src/grad.cpp
+++ b/imperative/python/src/grad.cpp
@@ -468,7 +468,7 @@ PyObject* GradKeyWrapper::get_priority() {
 }
 
 void GradKeyWrapper::set_priority(pybind11::handle priority) {
-    m_key->name = py::cast<int>(priority);
+    m_key->priority = py::cast<int>(priority);
 }
 
 void GradKeyWrapper::attach(PyObject*const* args, size_t nargs) {
@@ -535,7 +535,7 @@ void GradKey::backward(std::vector<TensorWrapper*> tensors, std::vector<TensorWr
         size_t priority_backup;
         CleanupGuard(GradKey* this_) : owner(this_) {
             priority_backup = sm_min_priority;
-            sm_min_priority = owner->priority;
+            sm_min_priority = owner->priority + 1;
         }
         ~CleanupGuard() {
             owner->cleanup();
@@ -636,7 +636,7 @@ PyObject* GradKeyWrapper::is_attached_to(PyObject*const* args, size_t nargs) {
     Py_RETURN_FALSE;
 }
 
-int GradKey::sm_min_priority = 0;
+int GradKey::sm_min_priority = std::numeric_limits<int>::min();
 
 GradKey::~GradKey() {
     cleanup();
diff --git a/imperative/python/src/tensor.cpp b/imperative/python/src/tensor.cpp
index 87c254e59e93d639ab9f90ac06fd3f4475181a7e..bec4cb77d642be507aa441510926e56be5ec288a 100644
--- a/imperative/python/src/tensor.cpp
+++ b/imperative/python/src/tensor.cpp
@@ -966,6 +966,7 @@ void init_tensor(py::module m) {
         .def<&GradKeyWrapper::attach>("attach")
         .def<&GradKeyWrapper::is_attached_to>("is_attached_to")
         .def_getset<&GradKeyWrapper::get_name, &GradKeyWrapper::set_name>("name")
+        .def_getset<&GradKeyWrapper::get_priority, &GradKeyWrapper::set_priority>("priority")
         .finalize();
     if (!grad_key_type) throw py::error_already_set();
     py::setattr(m, "GradKey", grad_key_type);
diff --git a/imperative/python/test/unit/autodiff/test_grad_manger.py b/imperative/python/test/unit/autodiff/test_grad_manger.py
index 6919a525ddf1b6277caf521cc1878f33f0cad779..2f82f6c0b9b48ec066f3be3a0e63533a08ca6790 100644
--- a/imperative/python/test/unit/autodiff/test_grad_manger.py
+++ b/imperative/python/test/unit/autodiff/test_grad_manger.py
@@ -279,3 +279,69 @@ def test_broadcast_grad(trace_mode):
         func()
 
     worker()
+
+
+def test_2nd_grad_with_manager():
+    x_np = np.random.rand(10).astype("float32")
+    x = mge.tensor(x_np)
+
+    gm = GradManager().attach([x])
+    gm2 = GradManager().attach([x])
+
+    with gm:
+        with gm2:
+            y = F.cos(x)
+            gm2.backward(y)
+        np.testing.assert_almost_equal(x.grad.numpy(), -np.sin(x_np), decimal=5)
+        gm.backward(x.grad)
+    np.testing.assert_almost_equal(
+        x.grad.numpy(), -np.sin(x_np) - np.cos(x_np), decimal=5
+    )
+
+
+def test_grad_manager_group():
+    x_np = np.random.rand(10).astype("float32")
+    x = mge.tensor(x_np)
+
+    gm = GradManager().attach([x])
+    gm2 = GradManager().attach([x])
+
+    with gm | gm2:
+        y = F.cos(x)
+        gm.backward(y)
+        gm2.backward(y)
+    np.testing.assert_almost_equal(x.grad.numpy(), -2 * np.sin(x_np), decimal=5)
+
+    x.grad = None
+
+
+def test_grad_manager_group_visibility():
+    x_np = np.random.rand(10).astype("float32")
+    x = mge.tensor(x_np)
+
+    gm = GradManager().attach([x])
+    gm2 = GradManager().attach([x])
+
+    with gm | gm2:
+        y = F.cos(x)
+        gm2.backward(y)
+        np.testing.assert_almost_equal(x.grad.numpy(), -np.sin(x_np), decimal=5)
+        gm.backward(x.grad)
+        np.testing.assert_almost_equal(x.grad.numpy(), -np.sin(x_np), decimal=5)
+
+
+def test_grad_manager_visibility_by_order():
+    x_np = np.random.rand(10).astype("float32")
+    x = mge.tensor(x_np)
+
+    gm = GradManager().attach([x])
+    gm2 = GradManager().attach([x])
+
+    with gm2:
+        with gm:
+            y = F.cos(x)
+            gm2.backward(y)
+            np.testing.assert_almost_equal(x.grad.numpy(), -np.sin(x_np), decimal=5)
+            gm.backward(x.grad)
+
+    np.testing.assert_almost_equal(x.grad.numpy(), -np.sin(x_np), decimal=5)
diff --git a/imperative/python/test/unit/core/test_autodiff.py b/imperative/python/test/unit/core/test_autodiff.py
index 248d7ca1bccbee6c016a8126587685ea5187716c..9765ba88d94d895613149630e084c41d6740eef9 100644
--- a/imperative/python/test/unit/core/test_autodiff.py
+++ b/imperative/python/test/unit/core/test_autodiff.py
@@ -126,7 +126,7 @@ def test_2nd_grad():
 
     x.grad = None
     grad2(z, ones)
-    np.testing.assert_almost_equal(x.grad.numpy(), -np.cos(x_np))
+    np.testing.assert_almost_equal(x.grad.numpy(), -np.cos(x_np), decimal=5)
 
 
 def test_grad_with_tensor_wrapper():