diff --git a/apscheduler/job.py b/apscheduler/job.py
index d676ca89..5c1b75d3 100644
--- a/apscheduler/job.py
+++ b/apscheduler/job.py
@@ -242,8 +242,9 @@ def __getstate__(self):
 
         # Instance methods cannot survive serialization as-is, so store the "self" argument
         # explicitly
-        if ismethod(self.func) and not isclass(self.func.__self__):
-            args = (self.func.__self__,) + tuple(self.args)
+        func = self.func
+        if ismethod(func) and not isclass(func.__self__) and obj_to_ref(func) == self.func_ref:
+            args = (func.__self__,) + tuple(self.args)
         else:
             args = self.args
 
diff --git a/tests/test_jobstores.py b/tests/test_jobstores.py
index f913f37e..132161bf 100644
--- a/tests/test_jobstores.py
+++ b/tests/test_jobstores.py
@@ -27,6 +27,9 @@ def dummy_classmethod(cls, a, b):
         return a + b
 
 
+dummy_instance = DummyClass()
+
+
 @pytest.fixture
 def memjobstore():
     yield MemoryJobStore()
@@ -112,19 +115,33 @@ def create(jobstore, func=dummy_job, run_date=datetime(2999, 1, 1), id=None, pau
     return create
 
 
-def test_add_instance_method_job(jobstore, create_add_job):
+def test_add_callable_instance_method_job(jobstore, create_add_job):
     instance = DummyClass()
     initial_job = create_add_job(jobstore, instance.dummy_method, kwargs={'a': 1, 'b': 2})
     job = jobstore.lookup_job(initial_job.id)
     assert job.func(*job.args, **job.kwargs) == 3
 
 
-def test_add_class_method_job(jobstore, create_add_job):
+def test_add_callable_class_method_job(jobstore, create_add_job):
     initial_job = create_add_job(jobstore, DummyClass.dummy_classmethod, kwargs={'a': 1, 'b': 2})
     job = jobstore.lookup_job(initial_job.id)
     assert job.func(*job.args, **job.kwargs) == 3
 
 
+def test_add_textual_instance_method_job(jobstore, create_add_job):
+    initial_job = create_add_job(jobstore, 'tests.test_jobstores:dummy_instance.dummy_method',
+                                 kwargs={'a': 1, 'b': 2})
+    job = jobstore.lookup_job(initial_job.id)
+    assert job.func(*job.args, **job.kwargs) == 3
+
+
+def test_add_textual_class_method_job(jobstore, create_add_job):
+    initial_job = create_add_job(jobstore, 'tests.test_jobstores:DummyClass.dummy_classmethod',
+                                 kwargs={'a': 1, 'b': 2})
+    job = jobstore.lookup_job(initial_job.id)
+    assert job.func(*job.args, **job.kwargs) == 3
+
+
 def test_lookup_job(jobstore, create_add_job):
     initial_job = create_add_job(jobstore)
     job = jobstore.lookup_job(initial_job.id)