diff --git a/pydantic/generics.py b/pydantic/generics.py
--- a/pydantic/generics.py
+++ b/pydantic/generics.py
@@ -30,6 +30,15 @@
 GenericModelT = TypeVar('GenericModelT', bound='GenericModel')
 TypeVarType = Any  # since mypy doesn't allow the use of TypeVar as a type
 
+Parametrization = Mapping[TypeVarType, Type[Any]]
+
+# _assigned_parameters is a Mapping from parametrized version of generic models to assigned types of parametrizations
+# as captured during construction of the class (not instances).
+# E.g., for generic model `Model[A, B]`, when parametrized model `Model[int, str]` is created,
+# `Model[int, str]`: {A: int, B: str}` will be stored in `_assigned_parameters`.
+# (This information is only otherwise available after creation from the class name string).
+_assigned_parameters: Dict[Type[Any], Parametrization] = {}
+
 
 class GenericModel(BaseModel):
     __slots__ = ()
@@ -86,13 +95,15 @@ def __class_getitem__(cls: Type[GenericModelT], params: Union[Type[Any], Tuple[T
             create_model(
                 model_name,
                 __module__=model_module or cls.__module__,
-                __base__=cls,
+                __base__=(cls,) + tuple(cls.__parameterized_bases__(typevars_map)),
                 __config__=None,
                 __validators__=validators,
                 **fields,
             ),
         )
 
+        _assigned_parameters[created_model] = typevars_map
+
         if called_globally:  # create global reference and therefore allow pickling
             object_by_reference = None
             reference_name = model_name
@@ -142,6 +153,70 @@ def __concrete_name__(cls: Type[Any], params: Tuple[Type[Any], ...]) -> str:
         params_component = ', '.join(param_names)
         return f'{cls.__name__}[{params_component}]'
 
+    @classmethod
+    def __parameterized_bases__(cls, typevars_map: Parametrization) -> Iterator[Type[Any]]:
+        """
+        Returns unbound bases of cls parameterised to given type variables
+
+        :param typevars_map: Dictionary of type applications for binding subclasses.
+            Given a generic class `Model` with 2 type variables [S, T]
+            and a concrete model `Model[str, int]`,
+            the value `{S: str, T: int}` would be passed to `typevars_map`.
+        :return: an iterator of generic sub classes, parameterised by `typevars_map`
+            and other assigned parameters of `cls`
+
+        e.g.:
+        ```
+        class A(GenericModel, Generic[T]):
+            ...
+
+        class B(A[V], Generic[V]):
+            ...
+
+        assert A[int] in B.__parameterized_bases__({V: int})
+        ```
+        """
+
+        def build_base_model(
+            base_model: Type[GenericModel], mapped_types: Parametrization
+        ) -> Iterator[Type[GenericModel]]:
+            base_parameters = tuple([mapped_types[param] for param in base_model.__parameters__])
+            parameterized_base = base_model.__class_getitem__(base_parameters)
+            if parameterized_base is base_model or parameterized_base is cls:
+                # Avoid duplication in MRO
+                return
+            yield parameterized_base
+
+        for base_model in cls.__bases__:
+            if not issubclass(base_model, GenericModel):
+                # not a class that can be meaningfully parameterized
+                continue
+            elif not getattr(base_model, '__parameters__', None):
+                # base_model is "GenericModel"  (and has no __parameters__)
+                # or
+                # base_model is already concrete, and will be included transitively via cls.
+                continue
+            elif cls in _assigned_parameters:
+                if base_model in _assigned_parameters:
+                    # cls is partially parameterised but not from base_model
+                    # e.g. cls = B[S], base_model = A[S]
+                    # B[S][int] should subclass A[int],  (and will be transitively via B[int])
+                    # but it's not viable to consistently subclass types with arbitrary construction
+                    # So don't attempt to include A[S][int]
+                    continue
+                else:  # base_model not in _assigned_parameters:
+                    # cls is partially parameterized, base_model is original generic
+                    # e.g.  cls = B[str, T], base_model = B[S, T]
+                    # Need to determine the mapping for the base_model parameters
+                    mapped_types: Parametrization = {
+                        key: typevars_map.get(value, value) for key, value in _assigned_parameters[cls].items()
+                    }
+                    yield from build_base_model(base_model, mapped_types)
+            else:
+                # cls is base generic, so base_class has a distinct base
+                # can construct the Parameterised base model using typevars_map directly
+                yield from build_base_model(base_model, typevars_map)
+
 
 def replace_types(type_: Any, type_map: Mapping[Any, Any]) -> Any:
     """Return type with all occurrences of `type_map` keys recursively replaced with their values.
diff --git a/pydantic/main.py b/pydantic/main.py
--- a/pydantic/main.py
+++ b/pydantic/main.py
@@ -877,7 +877,7 @@ def create_model(
     __model_name: str,
     *,
     __config__: Optional[Type[BaseConfig]] = None,
-    __base__: Type['Model'],
+    __base__: Union[Type['Model'], Tuple[Type['Model'], ...]],
     __module__: str = __name__,
     __validators__: Dict[str, classmethod] = None,
     **field_definitions: Any,
@@ -889,7 +889,7 @@ def create_model(
     __model_name: str,
     *,
     __config__: Optional[Type[BaseConfig]] = None,
-    __base__: Optional[Type['Model']] = None,
+    __base__: Union[None, Type['Model'], Tuple[Type['Model'], ...]] = None,
     __module__: str = __name__,
     __validators__: Dict[str, classmethod] = None,
     **field_definitions: Any,
@@ -910,8 +910,10 @@ def create_model(
     if __base__ is not None:
         if __config__ is not None:
             raise ConfigError('to avoid confusion __config__ and __base__ cannot be used together')
+        if not isinstance(__base__, tuple):
+            __base__ = (__base__,)
     else:
-        __base__ = cast(Type['Model'], BaseModel)
+        __base__ = (cast(Type['Model'], BaseModel),)
 
     fields = {}
     annotations = {}
@@ -942,7 +944,7 @@ def create_model(
     if __config__:
         namespace['Config'] = inherit_config(__config__, BaseConfig)
 
-    return type(__model_name, (__base__,), namespace)
+    return type(__model_name, __base__, namespace)
 
 
 _missing = object()

OK, after some digging, I've figured out why this is happening. Due to how `create_model` is called in `GenericModel.__class_getitem__`, we have the following class relationships:

* `ConcreteInnerClass[int] < ConcreteInnerClass[T]`
* `BaseInnerClass[int] < BaseInnerClass[T]`
* `ConcreteInnerClass[T] < BaseInnerClass[T]`

But we are missing the following:

* `ConcreteInnerClass[int] < BaseInnerClass[int]`
diff --git a/tests/test_generics.py b/tests/test_generics.py
--- a/tests/test_generics.py
+++ b/tests/test_generics.py
@@ -1160,6 +1160,92 @@ class SomeGenericModel(GenericModel, Generic[T]):
     SomeGenericModel[str](the_alias='qwe')
 
 
+@skip_36
+def test_generic_subclass():
+    T = TypeVar('T')
+
+    class A(GenericModel, Generic[T]):
+        ...
+
+    class B(A[T], Generic[T]):
+        ...
+
+    assert B[int].__name__ == 'B[int]'
+    assert issubclass(B[int], B)
+    assert issubclass(B[int], A[int])
+    assert not issubclass(B[int], A[str])
+
+
+@skip_36
+def test_generic_subclass_with_partial_application():
+    T = TypeVar('T')
+    S = TypeVar('S')
+
+    class A(GenericModel, Generic[T]):
+        ...
+
+    class B(A[S], Generic[T, S]):
+        ...
+
+    PartiallyAppliedB = B[str, T]
+    assert issubclass(PartiallyAppliedB[int], A[int])
+    assert not issubclass(PartiallyAppliedB[int], A[str])
+    assert not issubclass(PartiallyAppliedB[str], A[int])
+
+
+@skip_36
+def test_multilevel_generic_binding():
+    T = TypeVar('T')
+    S = TypeVar('S')
+
+    class A(GenericModel, Generic[T, S]):
+        ...
+
+    class B(A[str, T], Generic[T]):
+        ...
+
+    assert B[int].__name__ == 'B[int]'
+    assert issubclass(B[int], A[str, int])
+    assert not issubclass(B[str], A[str, int])
+
+
+@skip_36
+def test_generic_subclass_with_extra_type():
+    T = TypeVar('T')
+    S = TypeVar('S')
+
+    class A(GenericModel, Generic[T]):
+        ...
+
+    class B(A[S], Generic[T, S]):
+        ...
+
+    assert B[int, str].__name__ == 'B[int, str]', B[int, str].__name__
+    assert issubclass(B[str, int], B)
+    assert issubclass(B[str, int], A[int])
+    assert not issubclass(B[int, str], A[int])
+
+
+@skip_36
+def test_multi_inheritance_generic_binding():
+    T = TypeVar('T')
+
+    class A(GenericModel, Generic[T]):
+        ...
+
+    class B(A[int], Generic[T]):
+        ...
+
+    class C(B[str], Generic[T]):
+        ...
+
+    assert C[float].__name__ == 'C[float]'
+    assert issubclass(C[float], B[str])
+    assert not issubclass(C[float], B[int])
+    assert issubclass(C[float], A[int])
+    assert not issubclass(C[float], A[str])
+
+
 @skip_36
 def test_parse_generic_json():
     T = TypeVar('T')

GenericModel - Recursive abstract class fails validation
### Checks

* [x] I added a descriptive title to this issue
* [x] I have searched (google, github) for similar issues and couldn't find anything
* [x] I have read and followed [the docs](https://pydantic-docs.helpmanual.io/) and still think this is a bug

# Bug

Output of `python -c "import pydantic.utils; print(pydantic.utils.version_info())"`:
```
             pydantic version: 1.6.1
            pydantic compiled: False
                 install path: /wayfair/home/ch438l/pydantic/pydantic
               python version: 3.6.8 (default, Aug 10 2019, 06:54:07)  [GCC 4.8.5 20150623 (Red Hat 4.8.5-36)]
                     platform: Linux-3.10.0-862.3.2.el7.x86_64-x86_64-with-centos-7.5.1804-Core
     optional deps. installed: ['typing-extensions', 'email-validator', 'devtools']
```

If I try to define an attribute on a generic model to be a generic abstract class, then the model will fail to validate. Here's a failing test case:

```py
@skip_36
def test_abstract_generic_type_recursion():
    T = TypeVar('T')

    class BaseInnerClass(GenericModel, abc.ABC, Generic[T]):
        base_data: T

        @abc.abstractmethod
        def base_abstract(self) -> None:
            pass

    class ConcreteInnerClass(BaseInnerClass[T], Generic[T]):

        def base_abstract(self) -> None:
            return None

    class OuterClass(GenericModel, Generic[T]):
        inner_class: BaseInnerClass[T]

    OuterClass[int](inner_class=ConcreteInnerClass[int](base_data=2))
```

It appears to be failing because the `isinstance(value, cls)` check is failing for the generic type.

tests/test_generics.py::test_generic_subclass tests/test_generics.py::test_generic_subclass_with_partial_application tests/test_generics.py::test_multilevel_generic_binding tests/test_generics.py::test_generic_subclass_with_extra_type
tests/test_generics.py::test_generic_name tests/test_generics.py::test_double_parameterize_error tests/test_generics.py::test_value_validation tests/test_generics.py::test_methods_are_inherited tests/test_generics.py::test_config_is_inherited tests/test_generics.py::test_default_argument tests/test_generics.py::test_default_argument_for_typevar tests/test_generics.py::test_classvar tests/test_generics.py::test_non_annotated_field tests/test_generics.py::test_must_inherit_from_generic tests/test_generics.py::test_parameters_placed_on_generic tests/test_generics.py::test_parameters_must_be_typevar tests/test_generics.py::test_subclass_can_be_genericized tests/test_generics.py::test_parameter_count tests/test_generics.py::test_cover_cache tests/test_generics.py::test_generic_config tests/test_generics.py::test_enum_generic tests/test_generics.py::test_generic tests/test_generics.py::test_alongside_concrete_generics tests/test_generics.py::test_complex_nesting tests/test_generics.py::test_required_value tests/test_generics.py::test_optional_value tests/test_generics.py::test_custom_schema tests/test_generics.py::test_child_schema tests/test_generics.py::test_custom_generic_naming tests/test_generics.py::test_nested tests/test_generics.py::test_partial_specification tests/test_generics.py::test_partial_specification_with_inner_typevar tests/test_generics.py::test_partial_specification_name tests/test_generics.py::test_partial_specification_instantiation tests/test_generics.py::test_partial_specification_instantiation_bounded tests/test_generics.py::test_typevar_parametrization tests/test_generics.py::test_multiple_specification tests/test_generics.py::test_generic_subclass_of_concrete_generic tests/test_generics.py::test_generic_model_pickle tests/test_generics.py::test_generic_model_from_function_pickle_fail tests/test_generics.py::test_generic_model_redefined_without_cache_fail tests/test_generics.py::test_get_caller_frame_info tests/test_generics.py::test_get_caller_frame_info_called_from_module tests/test_generics.py::test_get_caller_frame_info_when_sys_getframe_undefined tests/test_generics.py::test_iter_contained_typevars tests/test_generics.py::test_nested_identity_parameterization tests/test_generics.py::test_replace_types tests/test_generics.py::test_replace_types_with_user_defined_generic_type_field tests/test_generics.py::test_replace_types_identity_on_unchanged tests/test_generics.py::test_deep_generic tests/test_generics.py::test_deep_generic_with_inner_typevar tests/test_generics.py::test_deep_generic_with_referenced_generic tests/test_generics.py::test_deep_generic_with_referenced_inner_generic tests/test_generics.py::test_deep_generic_with_multiple_typevars tests/test_generics.py::test_deep_generic_with_multiple_inheritance tests/test_generics.py::test_generic_with_referenced_generic_type_1 tests/test_generics.py::test_generic_with_referenced_nested_typevar tests/test_generics.py::test_generic_with_callable tests/test_generics.py::test_generic_with_partial_callable tests/test_generics.py::test_generic_recursive_models tests/test_generics.py::test_generic_enum tests/test_generics.py::test_generic_literal tests/test_generics.py::test_generic_enums tests/test_generics.py::test_generic_with_user_defined_generic_field tests/test_generics.py::test_generic_annotated tests/test_generics.py::test_multi_inheritance_generic_binding tests/test_generics.py::test_parse_generic_json