diff --git a/lower-constraints.txt b/lower-constraints.txt
index 2c33629b..9d96603d 100644
--- a/lower-constraints.txt
+++ b/lower-constraints.txt
@@ -16,8 +16,8 @@ isort==4.3.4
 Jinja2==2.10
 lazy-object-proxy==1.3.1
 linecache2==1.0.0
-lxml==3.4.1
-MarkupSafe==1.0
+lxml==4.5.0
+MarkupSafe==1.1.1
 mccabe==0.2.1
 mock==2.0.0
 openstackdocstheme==2.2.1
@@ -29,7 +29,7 @@ pylint==1.7.1
 python-mimeparse==1.6.0
 python-subunit==1.0.0
 pytz==2013.6
-PyYAML==3.12
+PyYAML==3.13
 reno==3.1.0
 requests==2.14.2
 restructuredtext-lint==1.1.1
diff --git a/requirements.txt b/requirements.txt
index 4ee2b521..b6318042 100644
--- a/requirements.txt
+++ b/requirements.txt
@@ -4,7 +4,7 @@
 
 pbr!=2.1.0,>=2.0.0 # Apache-2.0
 iso8601>=0.1.11 # MIT
-lxml!=3.7.0,>=3.4.1 # BSD
+lxml>=4.5.0 # BSD
 docutils>=0.11 # OSI-Approved Open Source, Public Domain
 sphinx>=2.0.0,!=2.1.0 # BSD
-PyYAML>=3.12 # MIT
+PyYAML>=3.13 # MIT