diff --git a/0001-pungi-Fix-tests-on-non-x86_64-arches.patch b/0001-pungi-Fix-tests-on-non-x86_64-arches.patch
new file mode 100644
index 00000000..5e3c461a
--- /dev/null
+++ b/0001-pungi-Fix-tests-on-non-x86_64-arches.patch
@@ -0,0 +1,36 @@
+From 3c1e2fba662cd635b20d2daf2c5acacfee407876 Mon Sep 17 00:00:00 2001
+From: =?UTF-8?q?Lubom=C3=ADr=20Sedl=C3=A1=C5=99?= <lsedlar@redhat.com>
+Date: Wed, 16 Nov 2016 09:20:10 +0100
+Subject: [PATCH] pungi: Fix tests on non-x86_64 arches
+MIME-Version: 1.0
+Content-Type: text/plain; charset=UTF-8
+Content-Transfer-Encoding: 8bit
+
+If the test did not specify an arch explicitly, it fell back on whatever
+arch the current machine has. This was causing failures when building
+RPM.
+
+Signed-off-by: Lubomír Sedlář <lsedlar@redhat.com>
+---
+ tests/test_pungi.py | 5 +++++
+ 1 file changed, 5 insertions(+)
+
+diff --git a/tests/test_pungi.py b/tests/test_pungi.py
+index a3297e7..d770d2a 100644
+--- a/tests/test_pungi.py
++++ b/tests/test_pungi.py
+@@ -65,6 +65,11 @@ class TestPungi(unittest.TestCase):
+         p.write_kickstart(self.ks, repos, groups, packages, prepopulate=prepopulate,
+                           multilib_whitelist=multilib_whitelist)
+         kwargs.setdefault('cache_dir', self.tmp_dir)
++        # Unless the test specifies an arch, we need to default to x86_64.
++        # Otherwise the arch of current machine will be used, which will cause
++        # failure most of the time.
++        kwargs.setdefault('arch', 'x86_64')
++
+         p.run_pungi(self.ks, self.tmp_dir, 'DP', **kwargs)
+         with open(self.out, "r") as f:
+             pkg_map = p.get_packages(f.read())
+-- 
+2.7.4
+
diff --git a/0002-pungi-Fix-incorrectly-skipped-tests.patch b/0002-pungi-Fix-incorrectly-skipped-tests.patch
new file mode 100644
index 00000000..bee99c11
--- /dev/null
+++ b/0002-pungi-Fix-incorrectly-skipped-tests.patch
@@ -0,0 +1,33 @@
+From b7813d34ac8e7986fbf2e8b1e4fc35427655ee8a Mon Sep 17 00:00:00 2001
+From: =?UTF-8?q?Lubom=C3=ADr=20Sedl=C3=A1=C5=99?= <lsedlar@redhat.com>
+Date: Wed, 16 Nov 2016 09:43:19 +0100
+Subject: [PATCH 2/2] pungi: Fix incorrectly skipped tests
+MIME-Version: 1.0
+Content-Type: text/plain; charset=UTF-8
+Content-Transfer-Encoding: 8bit
+
+The test was not correctly being skipped in Koji build, causing build
+failure.
+
+Signed-off-by: Lubomír Sedlář <lsedlar@redhat.com>
+---
+ tests/test_pungi.py | 3 +--
+ 1 file changed, 1 insertion(+), 2 deletions(-)
+
+diff --git a/tests/test_pungi.py b/tests/test_pungi.py
+index d770d2a..a519ddf 100644
+--- a/tests/test_pungi.py
++++ b/tests/test_pungi.py
+@@ -776,8 +776,7 @@ class TestPungi(unittest.TestCase):
+             "dummy-glibc-debuginfo-common-2.14-5.x86_64.rpm",
+         ])
+ 
+-    # This test is broken.
+-    @unittest.skip
++    @unittest.skip('This test is broken')
+     def test_bash_multilib_nogreedy(self):
+         packages = [
+             "dummy-bash.+",
+-- 
+2.7.4
+
diff --git a/pungi.spec b/pungi.spec
index 4eb3c48e..28cd987b 100644
--- a/pungi.spec
+++ b/pungi.spec
@@ -7,6 +7,9 @@ Group:          Development/Tools
 License:        GPLv2
 URL:            https://pagure.io/pungi
 Source0:        https://pagure.io/releases/%{name}/%{name}-%{version}.tar.bz2
+# These patches are added here to fix running tests. They are proposed in upstream as well.
+Patch0:         0001-pungi-Fix-tests-on-non-x86_64-arches.patch
+Patch1:         0002-pungi-Fix-incorrectly-skipped-tests.patch
 
 BuildRequires:  python-nose, python-nose-cov, python-mock
 BuildRequires:  python-devel, python-setuptools, python2-productmd
@@ -55,6 +58,8 @@ A tool to create anaconda based installation trees/isos of a set of rpms.
 
 %prep
 %setup -q
+%patch0 -p1
+%patch1 -p1
 
 %build
 %{__python} setup.py build