diff --git a/avoid-too-large-dates.patch b/avoid-too-large-dates.patch
new file mode 100644
index 0000000..4387cf9
--- /dev/null
+++ b/avoid-too-large-dates.patch
@@ -0,0 +1,105 @@
+--- a/tests/InCommon-metadata.xml
++++ b/tests/InCommon-metadata.xml
+@@ -1,4 +1,4 @@
+-<?xml version="1.0" encoding="UTF-8"?><EntitiesDescriptor xmlns="urn:oasis:names:tc:SAML:2.0:metadata" xmlns:ds="http://www.w3.org/2000/09/xmldsig#" xmlns:shibmd="urn:mace:shibboleth:metadata:1.0" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" ID="INC20140204T195141" Name="urn:mace:incommon" validUntil="2999-02-18T10:00:00Z" xsi:schemaLocation="urn:oasis:names:tc:SAML:2.0:metadata sstc-saml-schema-metadata-2.0.xsd urn:mace:shibboleth:metadata:1.0 shibboleth-metadata-1.0.xsd http://www.w3.org/2000/09/xmldsig# xmldsig-core-schema.xsd"><ds:Signature xmlns:ds="http://www.w3.org/2000/09/xmldsig#">
++<?xml version="1.0" encoding="UTF-8"?><EntitiesDescriptor xmlns="urn:oasis:names:tc:SAML:2.0:metadata" xmlns:ds="http://www.w3.org/2000/09/xmldsig#" xmlns:shibmd="urn:mace:shibboleth:metadata:1.0" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" ID="INC20140204T195141" Name="urn:mace:incommon" validUntil="2036-02-18T10:00:00Z" xsi:schemaLocation="urn:oasis:names:tc:SAML:2.0:metadata sstc-saml-schema-metadata-2.0.xsd urn:mace:shibboleth:metadata:1.0 shibboleth-metadata-1.0.xsd http://www.w3.org/2000/09/xmldsig# xmldsig-core-schema.xsd"><ds:Signature xmlns:ds="http://www.w3.org/2000/09/xmldsig#">
+ <ds:SignedInfo>
+ <ds:CanonicalizationMethod Algorithm="http://www.w3.org/2001/10/xml-exc-c14n#"/>
+ <ds:SignatureMethod Algorithm="http://www.w3.org/2001/04/xmldsig-more#rsa-sha256"/>
+--- a/tests/attribute_response.xml
++++ b/tests/attribute_response.xml
+@@ -32,13 +32,13 @@
+                     Method="urn:oasis:names:tc:SAML:2.0:cm:bearer">
+                 <saml2:SubjectConfirmationData Address="192.168.1.1"
+                                                InResponseTo="id-f4d370f3d03650f3ec0da694e2348bfe"
+-                                               NotOnOrAfter="2999-09-14T21:06:32.081Z"
++                                               NotOnOrAfter="2036-09-14T21:06:32.081Z"
+                                                Recipient="https://myreviewroom.com/saml2/acs/"
+                         />
+             </saml2:SubjectConfirmation>
+         </saml2:Subject>
+         <saml2:Conditions NotBefore="2014-09-14T21:01:32.081Z"
+-                          NotOnOrAfter="2999-09-14T21:06:32.081Z"
++                          NotOnOrAfter="2036-09-14T21:06:32.081Z"
+                 >
+             <saml2:AudienceRestriction>
+                 <saml2:Audience>urn:mace:example.com:saml:roland:sp
+--- a/tests/idp_example.xml
++++ b/tests/idp_example.xml
+@@ -2,7 +2,7 @@
+ <ns0:EntityDescriptor xmlns:ns0="urn:oasis:names:tc:SAML:2.0:metadata"
+                       xmlns:ns1="http://www.w3.org/2000/09/xmldsig#"
+                       entityID="http://localhost:8088/idp.xml"
+-                      validUntil="2014-04-12T06:06:13Z">
++                      validUntil="2036-04-12T06:06:13Z">
+     <ns0:IDPSSODescriptor WantAuthnRequestsOnlyWithValidCert="false"
+                           WantAuthnRequestsSigned="false"
+                           protocolSupportEnumeration="urn:oasis:names:tc:SAML:2.0:protocol">
+--- a/tests/metadata.aaitest.xml
++++ b/tests/metadata.aaitest.xml
+@@ -7,7 +7,7 @@
+                     xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance"
+                     ID="AAITest-20140205105921"
+                     Name="urn:mace:switch.ch:aaitest"
+-                    validUntil="2999-02-10T09:59:21Z"
++                    validUntil="2036-02-10T09:59:21Z"
+                     xsi:schemaLocation="urn:oasis:names:tc:SAML:2.0:metadata saml-schema-metadata-2.0.xsd urn:mace:shibboleth:metadata:1.0 shibboleth-metadata-1.0.xsd http://www.w3.org/2000/09/xmldsig# xmldsig-core-schema.xsd">
+     <ds:Signature xmlns:ds="http://www.w3.org/2000/09/xmldsig#">
+         <ds:SignedInfo>
+--- a/tests/metadata.xml
++++ b/tests/metadata.xml
+@@ -1,6 +1,6 @@
+ <?xml version='1.0' encoding='UTF-8'?>
+ <ns0:EntitiesDescriptor name="urn:mace:example.com:saml:test"
+-                        validUntil="2999-12-04T17:31:07Z"
++                        validUntil="2036-12-04T17:31:07Z"
+                         xmlns:ns0="urn:oasis:names:tc:SAML:2.0:metadata">
+   <ns0:EntityDescriptor entityID="urn:mace:example.com:saml:roland:sp">
+     <ns0:SPSSODescriptor AuthnRequestsSigned="False" WantAssertionsSigned="True"
+--- a/tests/metasp.xml
++++ b/tests/metasp.xml
+@@ -1,5 +1,5 @@
+ <?xml version="1.0" encoding="UTF-8"?>
+-<ns0:EntitiesDescriptor xmlns:ns0="urn:oasis:names:tc:SAML:2.0:metadata" name="urn:mace:umu.se:saml:test" validUntil="2010-12-01T09:22:16Z">
++<ns0:EntitiesDescriptor xmlns:ns0="urn:oasis:names:tc:SAML:2.0:metadata" name="urn:mace:umu.se:saml:test" validUntil="2036-12-01T09:22:16Z">
+   <ns0:EntityDescriptor entityID="urn:mace:umu.se:saml:roland:sp">
+     <ns0:SPSSODescriptor AuthnRequestsSigned="False" WantAssertionsSigned="True" protocolSupportEnumeration="urn:oasis:names:tc:SAML:2.0:protocol">
+       <ns0:KeyDescriptor>
+--- a/tests/remote_data/InCommon-metadata-export.xml
++++ b/tests/remote_data/InCommon-metadata-export.xml
+@@ -1,4 +1,4 @@
+-<?xml version="1.0" encoding="UTF-8" standalone="no"?><EntitiesDescriptor xmlns="urn:oasis:names:tc:SAML:2.0:metadata" xmlns:ds="http://www.w3.org/2000/09/xmldsig#" xmlns:md="urn:oasis:names:tc:SAML:2.0:metadata" xmlns:shibmd="urn:mace:shibboleth:metadata:1.0" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" ID="_20191126T193752" validUntil="3001-01-01T00:00:00Z">
++<?xml version="1.0" encoding="UTF-8" standalone="no"?><EntitiesDescriptor xmlns="urn:oasis:names:tc:SAML:2.0:metadata" xmlns:ds="http://www.w3.org/2000/09/xmldsig#" xmlns:md="urn:oasis:names:tc:SAML:2.0:metadata" xmlns:shibmd="urn:mace:shibboleth:metadata:1.0" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" ID="_20191126T193752" validUntil="2036-01-01T00:00:00Z">
+ <md:Extensions xmlns:mdrpi="urn:oasis:names:tc:SAML:metadata:rpi">
+ <mdrpi:PublicationInfo creationInstant="2019-11-26T19:37:52Z" publisher="https://incommon.org"/>
+ </md:Extensions>
+--- a/tests/swamid-2.0.xml
++++ b/tests/swamid-2.0.xml
+@@ -4,7 +4,7 @@
+       This file was automatically generated - do not edit 
+ 
+     -->
+-<md:EntitiesDescriptor xmlns:md="urn:oasis:names:tc:SAML:2.0:metadata" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns:ds="http://www.w3.org/2000/09/xmldsig#" xmlns:shibmd="urn:mace:shibboleth:metadata:1.0" Name="http://md.swamid.se/md/swamid-2.0.xml" cacheDuration="PT8H" validUntil="2999-12-13T10:05:05Z"><ds:Signature><ds:SignedInfo><ds:CanonicalizationMethod Algorithm="http://www.w3.org/TR/2001/REC-xml-c14n-20010315"/><ds:SignatureMethod Algorithm="http://www.w3.org/2000/09/xmldsig#rsa-sha1"/><ds:Reference URI=""><ds:Transforms><ds:Transform Algorithm="http://www.w3.org/2000/09/xmldsig#enveloped-signature"/><ds:Transform Algorithm="http://www.w3.org/2001/10/xml-exc-c14n#WithComments"/></ds:Transforms><ds:DigestMethod Algorithm="http://www.w3.org/2000/09/xmldsig#sha1"/><ds:DigestValue>wdokYz5tEa8aCh+fEPqytS/y9W8=</ds:DigestValue></ds:Reference></ds:SignedInfo><ds:SignatureValue>Wsr/+VrII3wK5rAzQKmjSzflCIuIhQboSc6sIxQwWw3toALPfY5fBl1XHPKGFXxY
++<md:EntitiesDescriptor xmlns:md="urn:oasis:names:tc:SAML:2.0:metadata" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns:ds="http://www.w3.org/2000/09/xmldsig#" xmlns:shibmd="urn:mace:shibboleth:metadata:1.0" Name="http://md.swamid.se/md/swamid-2.0.xml" cacheDuration="PT8H" validUntil="2036-12-13T10:05:05Z"><ds:Signature><ds:SignedInfo><ds:CanonicalizationMethod Algorithm="http://www.w3.org/TR/2001/REC-xml-c14n-20010315"/><ds:SignatureMethod Algorithm="http://www.w3.org/2000/09/xmldsig#rsa-sha1"/><ds:Reference URI=""><ds:Transforms><ds:Transform Algorithm="http://www.w3.org/2000/09/xmldsig#enveloped-signature"/><ds:Transform Algorithm="http://www.w3.org/2001/10/xml-exc-c14n#WithComments"/></ds:Transforms><ds:DigestMethod Algorithm="http://www.w3.org/2000/09/xmldsig#sha1"/><ds:DigestValue>wdokYz5tEa8aCh+fEPqytS/y9W8=</ds:DigestValue></ds:Reference></ds:SignedInfo><ds:SignatureValue>Wsr/+VrII3wK5rAzQKmjSzflCIuIhQboSc6sIxQwWw3toALPfY5fBl1XHPKGFXxY
+ t6W7MxPjU1FKh4PdISeTgqYUwvrX2YDE7HxoYAZR5n5cZlogBZIR3dUwXAcJ75pX
+ tDUHpoqNyEJgoaeTiFhNBrfwGPlWNb0RstfM+iMIpdNTlSFHvuHMxkJSEunjzbcj
+ 7OU8KcYSlosw4wqdI/G50aQAjSJf+M1wARHtbPvH9ULeks5AUhKyJYztrPJc1UJL
+--- a/tests/vo_metadata.xml
++++ b/tests/vo_metadata.xml
+@@ -1,11 +1,11 @@
+ <?xml version='1.0' encoding='UTF-8'?>
+-<ns0:EntitiesDescriptor 
+-  name="urn:mace:example.com:votest" 
+-  validUntil="2999-11-28T09:10:09Z"
++<ns0:EntitiesDescriptor
++  name="urn:mace:example.com:votest"
++  validUntil="2036-11-28T09:10:09Z"
+   xmlns:ns0="urn:oasis:names:tc:SAML:2.0:metadata">
+-  <ns0:EntityDescriptor 
++  <ns0:EntityDescriptor
+     entityID="urn:mace:example.com:it:tek">
+-    <ns0:AffiliationDescriptor 
++    <ns0:AffiliationDescriptor
+       affiliationOwnerID="http://vo.example.org/vo">
+       <ns0:AffiliateMember>
+         urn:mace:example.com:saml:aa
diff --git a/python-pysaml2.changes b/python-pysaml2.changes
index e762f08..caa9c82 100644
--- a/python-pysaml2.changes
+++ b/python-pysaml2.changes
@@ -1,3 +1,9 @@
+-------------------------------------------------------------------
+Wed Jan  6 10:49:48 UTC 2021 - Matej Cepl <mcepl@suse.com>
+
+- Add avoid-too-large-dates.patch to avoid test failures on i586
+  (Y38K bug; gh#IdentityPython/pysaml2#759)
+
 -------------------------------------------------------------------
 Mon Jan  4 21:25:04 UTC 2021 - Matej Cepl <mcepl@suse.com>
 
diff --git a/python-pysaml2.spec b/python-pysaml2.spec
index 5b49727..02a3a8d 100644
--- a/python-pysaml2.spec
+++ b/python-pysaml2.spec
@@ -26,6 +26,9 @@ Summary:        Python implementation of SAML Version 2 to be used in a WSGI env
 License:        Apache-2.0
 URL:            https://github.com/IdentityPython/pysaml2
 Source:         https://github.com/IdentityPython/pysaml2/archive/v%{version}.tar.gz
+# PATCH-FIX-UPSTREAM avoid-too-large-dates.patch gh#IdentityPython/pysaml2#759 mcepl@suse.com
+# avoid Y38K bug on 32bit machines.
+Patch0:         avoid-too-large-dates.patch
 BuildRequires:  %{python_module Paste}
 BuildRequires:  %{python_module cryptography >= 1.4}
 BuildRequires:  %{python_module dbm}
@@ -71,6 +74,10 @@ SAML2 service provider or an identity provider.
 
 %prep
 %setup -q -n %{modname}-%{version}
+%ifarch %{ix86}
+%patch0 -p1
+%endif
+
 # delete shebang of files not in executable path
 find src/ -name '*.py' -print0 | xargs -0 sed -i '1s/#!.*$//'
 # remove tests that poll internet