diff --git a/jedi/api/classes.py b/jedi/api/classes.py
index 130b492c..c5026b65 100644
--- a/jedi/api/classes.py
+++ b/jedi/api/classes.py
@@ -613,7 +613,7 @@ class Signature(Definition):
     return the `isinstance` function. without `(` it would return nothing.
     """
     def __init__(self, evaluator, signature):
-        super(CallSignature, self).__init__(evaluator, signature.name)
+        super(Signature, self).__init__(evaluator, signature.name)
         self._signature = signature
 
     @property
@@ -665,7 +665,11 @@ class ParamDefinition(Definition):
         return [Definition(self._evaluator, d.name) for d in self._name.infer_default()]
 
     def infer_annotation(self):
-        return [Definition(self._evaluator, d.name) for d in self._name.infer_annotation()]
+        return [Definition(self._evaluator, d.name)
+                for d in self._name.infer_annotation().execute_annotation()]
+
+    def to_string(self):
+        return self._name.to_string()
 
 
 def _format_signatures(context):
diff --git a/test/test_api/test_signatures.py b/test/test_api/test_signatures.py
new file mode 100644
index 00000000..23954369
--- /dev/null
+++ b/test/test_api/test_signatures.py
@@ -0,0 +1,21 @@
+import pytest
+
+
+@pytest.mark.parametrize(
+    'code, expected_params', [
+        ('def f(x: 1, y): ...\nf', [None, None]),
+        ('def f(x: int): ...\nf', ['instance int']),
+        ('from typing import List\ndef f(x: List[int]): ...\nf', ['instance list']),
+        ('from typing import Tuple\ndef f(x: Tuple[int]): ...\nf', ['Tuple: _SpecialForm = ...']),
+        ('x=str\ndef f(p: x): ...\nx=int\nf', ['instance int']),
+    ]
+)
+def test_param_annotation(Script, code, expected_params):
+    func, = Script(code).goto_assignments()
+    sig, = func.get_signatures()
+    for p, expected in zip(sig.params, expected_params):
+        if expected is None:
+            assert not p.infer_annotation()
+        else:
+            annotation, = p.infer_annotation()
+            assert annotation.description == expected