diff --git a/.github/workflows/tests.yml b/.github/workflows/tests.yml
index 622f20b3..0554d8b4 100644
--- a/.github/workflows/tests.yml
+++ b/.github/workflows/tests.yml
@@ -19,6 +19,7 @@ jobs:
           - {python: "3.10", postgres: "14"}
           - {python: "3.11", postgres: "15"}
           - {python: "3.12", postgres: "16"}
+          - {python: "3.13-dev", postgres: "16"}
 
           # Opposite extremes of the supported Py/PG range, other architecture
           - {python: "3.7", postgres: "16", architecture: "x86"}
@@ -27,6 +28,7 @@ jobs:
           - {python: "3.10", postgres: "13", architecture: "x86"}
           - {python: "3.11", postgres: "11", architecture: "x86"}
           - {python: "3.12", postgres: "10", architecture: "x86"}
+          - {python: "3.13-dev", postgres: "10", architecture: "x86"}
 
     env:
       PSYCOPG2_TESTDB: postgres
diff --git a/NEWS b/NEWS
index 5dec82fb..ce8c6aea 100644
--- a/NEWS
+++ b/NEWS
@@ -1,6 +1,12 @@
 Current release
 ---------------
 
+What's new in psycopg 2.9.10 (unreleased)
+^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
+
+- Add support for Python 3.13.
+
+
 What's new in psycopg 2.9.9
 ^^^^^^^^^^^^^^^^^^^^^^^^^^^
 
diff --git a/psycopg/utils.c b/psycopg/utils.c
index 16be9062..1dfb87d0 100644
--- a/psycopg/utils.c
+++ b/psycopg/utils.c
@@ -392,7 +392,10 @@ psyco_set_error(PyObject *exc, cursorObject *curs, const char *msg)
 static int
 psyco_is_main_interp(void)
 {
-#if PY_VERSION_HEX >= 0x03080000
+#if PY_VERSION_HEX >= 0x030d0000
+    /* tested with Python 3.13.0a6 */
+    return PyInterpreterState_Get() == PyInterpreterState_Main();
+#elif PY_VERSION_HEX >= 0x03080000
     /* tested with Python 3.8.0a2 */
     return _PyInterpreterState_Get() == PyInterpreterState_Main();
 #else
diff --git a/setup.py b/setup.py
index 37f6b5c0..7d1e30ba 100644
--- a/setup.py
+++ b/setup.py
@@ -58,6 +58,7 @@ Programming Language :: Python :: 3.9
 Programming Language :: Python :: 3.10
 Programming Language :: Python :: 3.11
 Programming Language :: Python :: 3.12
+Programming Language :: Python :: 3.13
 Programming Language :: Python :: 3 :: Only
 Programming Language :: Python :: Implementation :: CPython
 Programming Language :: C
diff --git a/tests/test_ipaddress.py b/tests/test_ipaddress.py
index 4a2339ef..3f803690 100755
--- a/tests/test_ipaddress.py
+++ b/tests/test_ipaddress.py
@@ -18,6 +18,7 @@
 
 from . import testutils
 import unittest
+import sys
 
 import psycopg2
 import psycopg2.extras
@@ -68,7 +69,12 @@ class NetworkingTestCase(testutils.ConnectingTestCase):
         self.assertEquals(cur.fetchone()[0], '127.0.0.1/24')
 
         cur.execute("select %s", [ip.ip_interface('::ffff:102:300/128')])
-        self.assertEquals(cur.fetchone()[0], '::ffff:102:300/128')
+
+        # The texual representation of addresses has changed in Python 3.13
+        if sys.version_info >= (3, 13):
+            self.assertEquals(cur.fetchone()[0], '::ffff:1.2.3.0/128')
+        else:
+            self.assertEquals(cur.fetchone()[0], '::ffff:102:300/128')
 
     @testutils.skip_if_crdb("cidr")
     def test_cidr_cast(self):
@@ -109,7 +115,12 @@ class NetworkingTestCase(testutils.ConnectingTestCase):
         self.assertEquals(cur.fetchone()[0], '127.0.0.0/24')
 
         cur.execute("select %s", [ip.ip_network('::ffff:102:300/128')])
-        self.assertEquals(cur.fetchone()[0], '::ffff:102:300/128')
+
+        # The texual representation of addresses has changed in Python 3.13
+        if sys.version_info >= (3, 13):
+            self.assertEquals(cur.fetchone()[0], '::ffff:1.2.3.0/128')
+        else:
+            self.assertEquals(cur.fetchone()[0], '::ffff:102:300/128')
 
 
 def test_suite():
diff --git a/tox.ini b/tox.ini
index 52ed80e3..ce450d3d 100644
--- a/tox.ini
+++ b/tox.ini
@@ -1,5 +1,5 @@
 [tox]
-envlist = {3.7,3.8,3.9,3.10,3.11,3.12}
+envlist = {3.7,3.8,3.9,3.10,3.11,3.12,3.13}
 
 [testenv]
 commands = make check