diff --git a/tensorflow/python/saved_model/function_deserialization.py b/tensorflow/python/saved_model/function_deserialization.py
index dccb222c26e..63fa4a4acbd 100644
--- a/tensorflow/python/saved_model/function_deserialization.py
+++ b/tensorflow/python/saved_model/function_deserialization.py
@@ -400,8 +400,11 @@ def fix_node_def(node_def, functions, shared_name_suffix, debug_name):
   if node_def.op in functions:
     node_def.op = functions[node_def.op].name
   for _, attr_value in node_def.attr.items():
-    if attr_value.func.name:
+    if attr_value.WhichOneof("value") == "func":
       attr_value.func.name = functions[attr_value.func.name].name
+    elif attr_value.WhichOneof("value") == "list":
+      for fn in attr_value.list.func:
+        fn.name = functions[fn.name].name
 
   # Fix old table creation bug.
   if node_def.op == "HashTableV2":
@@ -471,6 +474,10 @@ def _list_function_deps(fdef, library_function_names):
       for _, attr_value in node_def.attr.items():
         if attr_value.WhichOneof("value") == "func":
           deps.add(attr_value.func.name)
+        elif attr_value.WhichOneof("value") == "list":
+          for fn in attr_value.list.func:
+            deps.add(fn.name)
+
   return deps
 
 
diff --git a/tensorflow/python/saved_model/save_test.py b/tensorflow/python/saved_model/save_test.py
index 09e7296a483..f94cae8a4de 100644
--- a/tensorflow/python/saved_model/save_test.py
+++ b/tensorflow/python/saved_model/save_test.py
@@ -44,6 +44,7 @@ from tensorflow.python.keras.optimizer_v2 import adam
 from tensorflow.python.lib.io import file_io
 from tensorflow.python.module import module
 from tensorflow.python.ops import array_ops
+from tensorflow.python.ops import control_flow_ops
 from tensorflow.python.ops import lookup_ops
 from tensorflow.python.ops import math_ops
 from tensorflow.python.ops import resource_variable_ops
@@ -117,6 +118,24 @@ class SaveTest(test.TestCase):
         {"output_0": 2.},
         _import_and_infer(save_dir, {"x": 1.}))
 
+  def test_method_save_list_func(self):
+    root = tracking.AutoTrackable()
+
+    @def_function.function
+    def case_fn(x):
+      branch_index = constant_op.constant(1)
+      branches = [lambda: x, lambda: x + 1]
+      case_out = control_flow_ops.switch_case(branch_index, branches)
+      return case_out
+
+    root.f = def_function.function(
+        lambda x: 2. * case_fn(x),
+        input_signature=[tensor_spec.TensorSpec(None, dtypes.float32)])
+    root.f(constant_op.constant(1.))
+    save_dir = os.path.join(self.get_temp_dir(), "saved_model")
+    save.save(root, save_dir, root.f)
+    self.assertEqual({"output_0": 4.}, _import_and_infer(save_dir, {"x": 1.}))
+
   def test_method_save_concrete(self):
     root = tracking.AutoTrackable()
     root.f = def_function.function(