diff --git a/src/cattrs/gen.py b/src/cattrs/gen.py
index aedc4abf..db5c74e5 100644
--- a/src/cattrs/gen.py
+++ b/src/cattrs/gen.py
@@ -204,7 +204,17 @@ def _generate_mapping(
     cl: Type, old_mapping: Dict[str, type]
 ) -> Dict[str, type]:
     mapping = {}
-    for p, t in zip(get_origin(cl).__parameters__, get_args(cl)):
+
+    # To handle the cases where classes in the typing module are using
+    # the GenericAlias structure but aren’t a Generic and hence
+    # end up in this function but do not have an `__parameters__`
+    # attribute. These classes are interface types, for example
+    # `typing.Hashable`.
+    parameters = getattr(get_origin(cl), "__parameters__", None)
+    if parameters is None:
+        return old_mapping
+
+    for p, t in zip(parameters, get_args(cl)):
         if isinstance(t, TypeVar):
             continue
         mapping[p.__name__] = t
diff --git a/tests/test_converter_inheritance.py b/tests/test_converter_inheritance.py
index 4b694b6e..cb6db5de 100644
--- a/tests/test_converter_inheritance.py
+++ b/tests/test_converter_inheritance.py
@@ -1,3 +1,5 @@
+import collections
+import typing
 from typing import Type
 
 import attr
@@ -43,3 +45,58 @@ class B(A):
 
     # This should still work, but using the new hook instead.
     assert converter.structure({"i": 1}, B) == B(2)
+
+
+@pytest.mark.parametrize("converter_cls", [Converter, GenConverter])
+@pytest.mark.parametrize(
+    "typing_cls", [typing.Hashable, typing.Iterable, typing.Reversible]
+)
+def test_inherit_typing(converter_cls: Type[Converter], typing_cls):
+    """Stuff from typing.* resolves to runtime to collections.abc.*.
+
+    Hence, typing.* are of a special alias type which we want to check if
+    cattrs handles them correctly.
+    """
+    converter = converter_cls()
+
+    @attr.define
+    class A(typing_cls):
+        i: int = 0
+
+        def __hash__(self):
+            return hash(self.i)
+
+        def __iter__(self):
+            return iter([self.i])
+
+        def __reversed__(self):
+            return iter([self.i])
+
+    assert converter.structure({"i": 1}, A) == A(i=1)
+
+
+@pytest.mark.parametrize("converter_cls", [Converter, GenConverter])
+@pytest.mark.parametrize(
+    "collections_abc_cls",
+    [collections.abc.Hashable, collections.abc.Iterable, collections.abc.Reversible],
+)
+def test_inherit_collections_abc(
+    converter_cls: Type[Converter], collections_abc_cls
+):
+    """As extension of test_inherit_typing, check if collections.abc.* work."""
+    converter = converter_cls()
+
+    @attr.define
+    class A(collections_abc_cls):
+        i: int = 0
+
+        def __hash__(self):
+            return hash(self.i)
+
+        def __iter__(self):
+            return iter([self.i])
+
+        def __reversed__(self):
+            return iter([self.i])
+
+    assert converter.structure({"i": 1}, A) == A(i=1)