diff --git a/async_lru/__init__.py b/async_lru/__init__.py
index 447e9cdb..1ebbdcf8 100644
--- a/async_lru/__init__.py
+++ b/async_lru/__init__.py
@@ -9,6 +9,7 @@
     Coroutine,
     Generic,
     Hashable,
+    Literal,
     Optional,
     OrderedDict,
     Set,
@@ -63,8 +64,7 @@ def cancel(self) -> None:
             self.later_call = None
 
 
-@final
-class _LRUCacheWrapper(Generic[_R]):
+class _LRUCacheWrapperBase(Generic[_R]):
     def __init__(
         self,
         fn: _CB[_R],
@@ -161,8 +161,7 @@ def cache_parameters(self) -> _CacheParameters:
         )
 
     def _cache_hit(self, key: Hashable) -> None:
-        self.__hits += 1
-        self.__cache.move_to_end(key)
+        raise NotImplementedError("must be implemented by subclass")
 
     def _cache_miss(self, key: Hashable) -> None:
         self.__misses += 1
@@ -192,6 +191,23 @@ def _task_done_callback(
 
         fut.set_result(task.result())
 
+    async def __call__(self, /, *fn_args: Any, **fn_kwargs: Any) -> _R:
+        raise NotImplementedError("must be implemented by subclass")
+
+    def __get__(
+        self, instance: _T, owner: Optional[Type[_T]]
+    ) -> Union[Self, "_LRUCacheWrapperInstanceMethod[_R, _T]"]:
+        if owner is None:
+            return self
+        else:
+            return _LRUCacheWrapperInstanceMethod(self, instance)
+
+@final
+class _LRUCacheWrapper(_LRUCacheWrapperBase[_R]):
+    def _cache_hit(self, key: Hashable) -> None:
+        self.__hits += 1
+        self.__cache.move_to_end(key)
+
     async def __call__(self, /, *fn_args: Any, **fn_kwargs: Any) -> _R:
         if self.__closed:
             raise RuntimeError(f"alru_cache is closed for {self}")
@@ -217,20 +233,44 @@ async def __call__(self, /, *fn_args: Any, **fn_kwargs: Any) -> _R:
 
         self.__cache[key] = _CacheItem(fut, None)
 
-        if self.__maxsize is not None and len(self.__cache) > self.__maxsize:
+        if len(self.__cache) > self.__maxsize:
             dropped_key, cache_item = self.__cache.popitem(last=False)
             cache_item.cancel()
 
         self._cache_miss(key)
         return await asyncio.shield(fut)
+    
+@final
+class _LRUCacheWrapperUnbounded(_LRUCacheWrapperBase[_R]):
+    def _cache_hit(self, key: Hashable) -> None:
+        self.__hits += 1
 
-    def __get__(
-        self, instance: _T, owner: Optional[Type[_T]]
-    ) -> Union[Self, "_LRUCacheWrapperInstanceMethod[_R, _T]"]:
-        if owner is None:
-            return self
-        else:
-            return _LRUCacheWrapperInstanceMethod(self, instance)
+    async def __call__(self, /, *fn_args: Any, **fn_kwargs: Any) -> _R:
+        if self.__closed:
+            raise RuntimeError(f"alru_cache is closed for {self}")
+
+        loop = asyncio.get_running_loop()
+
+        key = _make_key(fn_args, fn_kwargs, self.__typed)
+
+        cache_item = self.__cache.get(key)
+
+        if cache_item is not None:
+            self._cache_hit(key)
+            if not cache_item.fut.done():
+                return await asyncio.shield(cache_item.fut)
+
+            return cache_item.fut.result()
+
+        fut = loop.create_future()
+        coro = self.__wrapped__(*fn_args, **fn_kwargs)
+        task: asyncio.Task[_R] = loop.create_task(coro)
+        self.__tasks.add(task)
+        task.add_done_callback(partial(self._task_done_callback, fut, key))
+
+        self.__cache[key] = _CacheItem(fut, None)
+        self._cache_miss(key)
+        return await asyncio.shield(fut)
 
 
 @final
@@ -293,11 +333,32 @@ async def __call__(self, /, *fn_args: Any, **fn_kwargs: Any) -> _R:
         return await self.__wrapper(self.__instance, *fn_args, **fn_kwargs)
 
 
+@overload
 def _make_wrapper(
-    maxsize: Optional[int],
+    maxsize: int,
     typed: bool,
     ttl: Optional[float] = None,
 ) -> Callable[[_CBP[_R]], _LRUCacheWrapper[_R]]:
+    ...
+
+
+@overload
+def _make_wrapper(
+    maxsize: Literal[None],
+    typed: bool,
+    ttl: Optional[float] = None,
+) -> Callable[[_CBP[_R]], _LRUCacheWrapperUnbounded[_R]]:
+    ...
+
+
+def _make_wrapper(
+    maxsize: Optional[int],
+    typed: bool,
+    ttl: Optional[float] = None,
+) -> Union[
+    Callable[[_CBP[_R]], _LRUCacheWrapper[_R]],
+    Callable[[_CBP[_R]], _LRUCacheWrapperUnbounded[_R]],
+]:
     def wrapper(fn: _CBP[_R]) -> _LRUCacheWrapper[_R]:
         origin = fn
 
@@ -311,7 +372,8 @@ def wrapper(fn: _CBP[_R]) -> _LRUCacheWrapper[_R]:
         if hasattr(fn, "_make_unbound_method"):
             fn = fn._make_unbound_method()
 
-        wrapper = _LRUCacheWrapper(cast(_CB[_R], fn), maxsize, typed, ttl)
+        wrapper_cls = _LRUCacheWrapperUnbounded if maxsize is None else _LRUCacheWrapper
+        wrapper = wrapper_cls(cast(_CB[_R], fn), maxsize, typed, ttl)
         if sys.version_info >= (3, 12):
             wrapper = inspect.markcoroutinefunction(wrapper)
         return wrapper
@@ -319,6 +381,16 @@ def wrapper(fn: _CBP[_R]) -> _LRUCacheWrapper[_R]:
     return wrapper
 
 
+@overload
+def alru_cache(
+    maxsize: Literal[None],
+    typed: bool = False,
+    *,
+    ttl: Optional[float] = None,
+) -> Callable[[_CBP[_R]], _LRUCacheWrapperUnbounded[_R]]:
+    ...
+
+
 @overload
 def alru_cache(
     maxsize: Optional[int] = 128,
@@ -342,7 +414,11 @@ def alru_cache(
     typed: bool = False,
     *,
     ttl: Optional[float] = None,
-) -> Union[Callable[[_CBP[_R]], _LRUCacheWrapper[_R]], _LRUCacheWrapper[_R]]:
+) -> Union[
+    Callable[[_CBP[_R]], _LRUCacheWrapper[_R]],
+    Callable[[_CBP[_R]], _LRUCacheWrapperUnbounded[_R]],
+    _LRUCacheWrapper[_R],
+]:
     if maxsize is None or isinstance(maxsize, int):
         return _make_wrapper(maxsize, typed, ttl)
     else: