diff --git a/0001-always-obey-GEVENT_NO_CFFI_BUILD.patch b/0001-always-obey-GEVENT_NO_CFFI_BUILD.patch
deleted file mode 100644
index 7f768ec..0000000
--- a/0001-always-obey-GEVENT_NO_CFFI_BUILD.patch
+++ /dev/null
@@ -1,42 +0,0 @@
-From 05650624fe2524ecb1bdbbd4facc5d988275e542 Mon Sep 17 00:00:00 2001
-From: Dan Callaghan <dcallagh@redhat.com>
-Date: Wed, 7 Jun 2017 13:55:53 +1000
-Subject: [PATCH] always obey GEVENT_NO_CFFI_BUILD
-
-If libev is not embedded, we still want to set GEVENT_NO_CFFI_BUILD=1 to
-prevent setup.py from trying to configure libev, regardless whether cffi
-modules will actually be built or not.
----
- setup.py | 11 ++++++-----
- 1 file changed, 6 insertions(+), 5 deletions(-)
-
-diff --git a/setup.py b/setup.py
-index 9c229ad..ea4dcaf 100755
---- a/setup.py
-+++ b/setup.py
-@@ -90,16 +90,17 @@
- except ImportError:
-     pass
- else:
--    if IGNORE_CFFI and not PYPY:
--        # Allow distributors to turn off CFFI builds
--        # even if it's available, because CFFI always embeds
--        # our copy of libev and they may not want that.
--        del cffi_modules[:]
-     # Note that we don't add cffi to install_requires, it's
-     # optional. We tend to build and distribute wheels with the CFFI
-     # modules built and they can be imported if CFFI is installed.
-     # install_requires.append('cffi >= 1.3.0')
-+    pass
- 
-+if IGNORE_CFFI and not PYPY:
-+    # Allow distributors to turn off CFFI builds
-+    # even if it's available, because CFFI always embeds
-+    # our copy of libev and they may not want that.
-+    del cffi_modules[:]
- 
- # If we are running info / help commands, or we're being imported by
- # tools like pyroma, we don't need to build anything
--- 
-2.9.4
-
diff --git a/0001-code-replace.patch b/0001-code-replace.patch
new file mode 100644
index 0000000..8cbbe02
--- /dev/null
+++ b/0001-code-replace.patch
@@ -0,0 +1,26 @@
+commit 1b84da94c2aa2d171881482c22298ad189b79764
+Author: Victor Stinner <vstinner@redhat.com>
+Date:   Tue Jun 11 16:38:52 2019 +0200
+
+    Use CodeType.replace() if available
+    
+    Port _tblib.Traceback to Python 3.8: use code.replace() method if
+    available.
+
+diff --git a/src/gevent/_tblib.py b/src/gevent/_tblib.py
+index 13364012..b9553a9e 100644
+--- a/src/gevent/_tblib.py
++++ b/src/gevent/_tblib.py
+@@ -198,7 +198,11 @@ class Traceback(object):
+         while current:
+             f_code = current.tb_frame.f_code
+             code = compile('\n' * (current.tb_lineno - 1) + 'raise __traceback_maker', current.tb_frame.f_code.co_filename, 'exec')
+-            if PY3:
++            if hasattr(code, "replace"):
++                # Python 3.8 and newer
++                code = code.replace(co_argcount=0,
++                                    co_freevars=(), co_cellvars=())
++            elif PY3:
+                 code = CodeType(
+                     0, code.co_kwonlyargcount,
+                     code.co_nlocals, code.co_stacksize, code.co_flags,
diff --git a/python-gevent.spec b/python-gevent.spec
index a115ea8..527f586 100644
--- a/python-gevent.spec
+++ b/python-gevent.spec
@@ -4,13 +4,18 @@
 
 Name:          python-%{modname}
 Version:       1.3.6
-Release:       2%{?dist}
+Release:       3%{?dist}
 Summary:       A coroutine-based Python networking library
 
 License:       MIT
 URL:           http://www.gevent.org/
 Source0:       https://files.pythonhosted.org/packages/source/g/%{modname}/%{modname}-%{version}.tar.gz
 
+# Python 3.8 compatibility: use code.replace() method
+# https://github.com/gevent/gevent/pull/1429
+# https://github.com/gevent/gevent/commit/806713333afa9d490d31c0f9b534031c07467fc7
+Patch1:        0001-code-replace.patch
+
 BuildRequires:  gcc
 BuildRequires: c-ares-devel
 BuildRequires: libev-devel
@@ -74,7 +79,7 @@ Features include:
 Python 3 version.
 
 %prep
-%autosetup -n %{modname}-%{version}
+%autosetup -p1 -n %{modname}-%{version}
 # Remove bundled libraries
 rm -r deps
 # Upstream intentionally includes C extension sources in the built package, 
@@ -117,6 +122,10 @@ find %{buildroot} -name '*.so' -exec chmod 755 {} ';'
 %{python3_sitearch}/%{modname}*
 
 %changelog
+* Tue Jun 11 2019 Victor Stinner <vstinner@redhat.com> - 1.3.6-3
+- Add Python 3.8 support, backport upstream change to use CodeType.replace() if
+  available (rhbz#1716342)
+
 * Sat Feb 02 2019 Fedora Release Engineering <releng@fedoraproject.org> - 1.3.6-2
 - Rebuilt for https://fedoraproject.org/wiki/Fedora_30_Mass_Rebuild