diff --git a/ming/odm/mapper.pyi b/ming/odm/mapper.pyi
index 8598cf8..6460c21 100644
--- a/ming/odm/mapper.pyi
+++ b/ming/odm/mapper.pyi
@@ -1,4 +1,4 @@
-from typing import type_check_only, TypeVar, Generic, Optional, Union, Any, Dict
+from typing import type_check_only, TypeVar, Generic, Optional, Union, Any, Dict, overload
 
 from bson import ObjectId
 from ming.base import Cursor
@@ -12,10 +12,9 @@ class _ClassQuery(Generic[M]):
     def get(self, _id: Union[ObjectId|Any] = None, **kwargs) -> Optional[M]: ...
     def find(self, filter: MongoFilter = None, *args, **kwargs) -> Cursor[M]: ...
     def find_by(self, filter: MongoFilter = None, *args, **kwargs) -> Cursor[M]: ...
-    def remove(self, spec_or_id: Union[MongoFilter, ObjectId], **kwargs) -> ChangeResult: ...
+    def remove(self, spec_or_id: Union[MongoFilter, ObjectId] = None, **kwargs) -> ChangeResult: ...
     def count(self) -> int: ...
     def find_and_modify(self, **kwargs) -> M: ...
-    def update(self, spec: MongoFilter, fields: dict, **kwargs) -> ChangeResult: ...
     """
     def group(self) -> int: ...
     def distinct(self) -> int: ...
@@ -29,10 +28,15 @@ class _InstQuery(object):
     def update_if_not_modified(self, obj, fields, upsert=False) -> bool: ...
 
     def delete(self) -> ChangeResult: ...
-    def update(self, fields, **kwargs) -> ChangeResult: ...
 
 @type_check_only
-class Query(_ClassQuery[M], _InstQuery): ...
+class Query(_ClassQuery[M], _InstQuery):
+
+    @overload  # from _ClassQuery
+    def update(self, spec: MongoFilter, fields: dict, **kwargs) -> ChangeResult: ...
+
+    @overload  # from _InstQuery
+    def update(self, fields, **kwargs) -> ChangeResult: ...
 
 
 def __getattr__(name) -> Any: ...  # marks file as incomplete
\ No newline at end of file
diff --git a/ming/odm/property.pyi b/ming/odm/property.pyi
index f140054..a79b796 100644
--- a/ming/odm/property.pyi
+++ b/ming/odm/property.pyi
@@ -12,15 +12,15 @@ MC = TypeVar('MC', bound=MappedClass)
 
 class ForeignIdProperty:
     @overload
-    def __new__(self, related: Type, uselist=False, allow_none=False, *args, **kwargs) -> ObjectId: ...
+    def __new__(self, related: Type[MC], uselist=False, allow_none=False, *args, **kwargs) -> ObjectId: ...
     @overload
-    def __new__(self, related: TypeAlias, uselist=False, allow_none=False, *args, **kwargs) -> ObjectId: ...
+    def __new__(self, related: str, uselist=False, allow_none=False, *args, **kwargs) -> ObjectId: ...
 
 class RelationProperty:
     @overload
-    def __new__(self, related: TypeAlias, via: str=None, fetch=True) -> Any:...
+    def __new__(self, related: str, via: str=None, fetch=True) -> Any:...
     @overload
-    def __new__(self, related: MC, via: str=None, fetch=True) -> MC:...
+    def __new__(self, related: Type[MC], via: str=None, fetch=True) -> MC:...
 
 
 def __getattr__(name) -> Any: ...  # marks file as incomplete
\ No newline at end of file