diff --git a/starlette/applications.py b/starlette/applications.py
index a46cbaa0e..c68ad864a 100644
--- a/starlette/applications.py
+++ b/starlette/applications.py
@@ -65,7 +65,7 @@ def __init__(
             on_startup is None and on_shutdown is None
         ), "Use either 'lifespan' or 'on_startup'/'on_shutdown', not both."
 
-        self._debug = debug
+        self.debug = debug
         self.state = State()
         self.router = Router(
             routes, on_startup=on_startup, on_shutdown=on_shutdown, lifespan=lifespan
@@ -74,7 +74,7 @@ def __init__(
             {} if exception_handlers is None else dict(exception_handlers)
         )
         self.user_middleware = [] if middleware is None else list(middleware)
-        self.middleware_stack = self.build_middleware_stack()
+        self.middleware_stack: typing.Optional[ASGIApp] = None
 
     def build_middleware_stack(self) -> ASGIApp:
         debug = self.debug
@@ -108,20 +108,13 @@ def build_middleware_stack(self) -> ASGIApp:
     def routes(self) -> typing.List[BaseRoute]:
         return self.router.routes
 
-    @property
-    def debug(self) -> bool:
-        return self._debug
-
-    @debug.setter
-    def debug(self, value: bool) -> None:
-        self._debug = value
-        self.middleware_stack = self.build_middleware_stack()
-
     def url_path_for(self, name: str, **path_params: typing.Any) -> URLPath:
         return self.router.url_path_for(name, **path_params)
 
     async def __call__(self, scope: Scope, receive: Receive, send: Send) -> None:
         scope["app"] = self
+        if self.middleware_stack is None:
+            self.middleware_stack = self.build_middleware_stack()
         await self.middleware_stack(scope, receive, send)
 
     def on_event(self, event_type: str) -> typing.Callable:  # pragma: nocover
@@ -137,11 +130,10 @@ def host(
     ) -> None:  # pragma: no cover
         self.router.host(host, app=app, name=name)
 
-    def add_middleware(
-        self, middleware_class: type, **options: typing.Any
-    ) -> None:  # pragma: no cover
+    def add_middleware(self, middleware_class: type, **options: typing.Any) -> None:
+        if self.middleware_stack is not None:  # pragma: no cover
+            raise RuntimeError("Cannot add middleware after an application has started")
         self.user_middleware.insert(0, Middleware(middleware_class, **options))
-        self.middleware_stack = self.build_middleware_stack()
 
     def add_exception_handler(
         self,
@@ -149,7 +141,6 @@ def add_exception_handler(
         handler: typing.Callable,
     ) -> None:  # pragma: no cover
         self.exception_handlers[exc_class_or_status_code] = handler
-        self.middleware_stack = self.build_middleware_stack()
 
     def add_event_handler(
         self, event_type: str, func: typing.Callable
diff --git a/tests/test_applications.py b/tests/test_applications.py
index fcacbe633..ba10aff8e 100644
--- a/tests/test_applications.py
+++ b/tests/test_applications.py
@@ -1,7 +1,9 @@
 import os
 from contextlib import asynccontextmanager
+from typing import Any, Callable
 
 import anyio
+import httpx
 import pytest
 
 from starlette import status
@@ -13,6 +15,7 @@
 from starlette.responses import JSONResponse, PlainTextResponse
 from starlette.routing import Host, Mount, Route, Router, WebSocketRoute
 from starlette.staticfiles import StaticFiles
+from starlette.types import ASGIApp
 from starlette.websockets import WebSocket
 
 
@@ -486,3 +489,45 @@ async def startup():
 
         app.on_event("startup")(startup)
         assert len(record) == 1
+
+
+def test_middleware_stack_init(test_client_factory: Callable[[ASGIApp], httpx.Client]):
+    class NoOpMiddleware:
+        def __init__(self, app: ASGIApp):
+            self.app = app
+
+        async def __call__(self, *args: Any):
+            await self.app(*args)
+
+    class SimpleInitializableMiddleware:
+        counter = 0
+
+        def __init__(self, app: ASGIApp):
+            self.app = app
+            SimpleInitializableMiddleware.counter += 1
+
+        async def __call__(self, *args: Any):
+            await self.app(*args)
+
+    def get_app() -> ASGIApp:
+        app = Starlette()
+        app.add_middleware(SimpleInitializableMiddleware)
+        app.add_middleware(NoOpMiddleware)
+        return app
+
+    app = get_app()
+
+    with test_client_factory(app):
+        pass
+
+    assert SimpleInitializableMiddleware.counter == 1
+
+    test_client_factory(app).get("/foo")
+
+    assert SimpleInitializableMiddleware.counter == 1
+
+    app = get_app()
+
+    test_client_factory(app).get("/foo")
+
+    assert SimpleInitializableMiddleware.counter == 2