diff --git a/.github/workflows/test-suite.yml b/.github/workflows/test-suite.yml
index 0bb570ced..fac946039 100644
--- a/.github/workflows/test-suite.yml
+++ b/.github/workflows/test-suite.yml
@@ -14,7 +14,7 @@ jobs:
 
     strategy:
       matrix:
-        python-version: ["3.8", "3.9", "3.10", "3.11", "3.12"]
+        python-version: ["3.8", "3.9", "3.10", "3.11", "3.12", "3.13"]
 
     steps:
       - uses: "actions/checkout@v4"
diff --git a/pyproject.toml b/pyproject.toml
index b1271db8d..f2721c870 100644
--- a/pyproject.toml
+++ b/pyproject.toml
@@ -23,6 +23,7 @@ classifiers = [
     "Programming Language :: Python :: 3.10",
     "Programming Language :: Python :: 3.11",
     "Programming Language :: Python :: 3.12",
+    "Programming Language :: Python :: 3.13",
     "Topic :: Internet :: WWW/HTTP",
 ]
 dependencies = [
diff --git a/starlette/middleware/errors.py b/starlette/middleware/errors.py
index e9eba62b0..3fc4a4402 100644
--- a/starlette/middleware/errors.py
+++ b/starlette/middleware/errors.py
@@ -2,6 +2,7 @@
 
 import html
 import inspect
+import sys
 import traceback
 import typing
 
@@ -237,11 +238,13 @@ def generate_html(self, exc: Exception, limit: int = 7) -> str:
                 exc_html += self.generate_frame_html(frame, is_collapsed)
                 is_collapsed = True
 
+        if sys.version_info >= (3, 13):  # pragma: no cover
+            exc_type_str = traceback_obj.exc_type_str
+        else:  # pragma: no cover
+            exc_type_str = traceback_obj.exc_type.__name__
+
         # escape error class and text
-        error = (
-            f"{html.escape(traceback_obj.exc_type.__name__)}: "
-            f"{html.escape(str(traceback_obj))}"
-        )
+        error = f"{html.escape(exc_type_str)}: {html.escape(str(traceback_obj))}"
 
         return TEMPLATE.format(styles=STYLES, js=JS, error=error, exc_html=exc_html)
 
diff --git a/starlette/middleware/gzip.py b/starlette/middleware/gzip.py
index cbb0f4a5b..0579e0410 100644
--- a/starlette/middleware/gzip.py
+++ b/starlette/middleware/gzip.py
@@ -41,7 +41,8 @@ def __init__(self, app: ASGIApp, minimum_size: int, compresslevel: int = 9) -> N
 
     async def __call__(self, scope: Scope, receive: Receive, send: Send) -> None:
         self.send = send
-        await self.app(scope, receive, self.send_with_gzip)
+        with self.gzip_buffer, self.gzip_file:
+            await self.app(scope, receive, self.send_with_gzip)
 
     async def send_with_gzip(self, message: Message) -> None:
         message_type = message["type"]