diff --git a/lower-constraints.txt b/lower-constraints.txt
index 3fb0252734a2..ff6b310fe160 100644
--- a/lower-constraints.txt
+++ b/lower-constraints.txt
@@ -7,7 +7,7 @@ automaton==1.14.0
 bandit==1.1.0
 cachetools==2.0.1
 castellan==0.16.0
-cffi==1.11.5
+cffi==1.14.0
 cliff==2.11.0
 cmd2==0.8.1
 colorama==0.3.9
@@ -30,7 +30,7 @@ futurist==1.8.0
 gabbi==1.35.0
 gitdb2==2.0.3
 GitPython==2.1.8
-greenlet==0.4.10
+greenlet==0.4.15
 idna==2.6
 iso8601==0.1.11
 Jinja2==2.10
@@ -44,9 +44,9 @@ keystoneauth1==3.16.0
 keystonemiddleware==4.20.0
 kombu==4.6.1
 linecache2==1.0.0
-lxml==3.4.1
+lxml==4.5.0
 Mako==1.0.7
-MarkupSafe==1.0
+MarkupSafe==1.1.1
 microversion-parse==0.2.1
 mock==3.0.0
 msgpack==0.5.6
@@ -56,7 +56,7 @@ mypy==0.761
 netaddr==0.7.18
 netifaces==0.10.4
 networkx==2.1.0
-numpy==1.14.2
+numpy==1.19.0
 openstacksdk==0.35.0
 os-brick==3.1.0
 os-client-config==1.29.0
@@ -91,7 +91,7 @@ osprofiler==1.4.0
 ovs==2.10.0
 ovsdbapp==0.15.0
 packaging==17.1
-paramiko==2.0.0
+paramiko==2.7.1
 Paste==2.0.2
 PasteDeploy==1.5.0
 pbr==2.0.0
@@ -99,7 +99,7 @@ pluggy==0.6.0
 ply==3.11
 prettytable==0.7.1
 psutil==3.2.2
-psycopg2==2.7
+psycopg2==2.8
 py==1.5.2
 pyasn1==0.4.2
 pyasn1-modules==0.2.1
@@ -108,7 +108,7 @@ pycparser==2.18
 pyinotify==0.9.6
 pyroute2==0.5.4
 PyJWT==1.7.0
-PyMySQL==0.7.6
+PyMySQL==0.8.0
 pyOpenSSL==17.5.0
 pyparsing==2.2.0
 pyperclip==1.6.0
@@ -125,7 +125,7 @@ python-mimeparse==1.6.0
 python-neutronclient==6.7.0
 python-subunit==1.4.0
 pytz==2018.3
-PyYAML==3.12
+PyYAML==3.13
 repoze.lru==0.7
 requests==2.14.2
 requests-mock==1.2.0
diff --git a/requirements.txt b/requirements.txt
index f33c2b40630f..6e27dca79360 100644
--- a/requirements.txt
+++ b/requirements.txt
@@ -8,20 +8,20 @@ decorator>=4.1.0 # BSD
 eventlet>=0.22.0 # MIT
 Jinja2>=2.10 # BSD License (3 clause)
 keystonemiddleware>=4.20.0 # Apache-2.0
-lxml!=3.7.0,>=3.4.1 # BSD
+lxml>=4.5.0 # BSD
 Routes>=2.3.1 # MIT
 cryptography>=2.7 # BSD/Apache-2.0
 WebOb>=1.8.2 # MIT
 # NOTE(mriedem): greenlet 0.4.14 does not work with older versions of gcc on
 # ppc64le systems, see https://github.com/python-greenlet/greenlet/issues/136.
-greenlet>=0.4.10,!=0.4.14 # MIT
+greenlet>=0.4.15 # MIT
 PasteDeploy>=1.5.0 # MIT
 Paste>=2.0.2 # MIT
 PrettyTable<0.8,>=0.7.1 # BSD
 sqlalchemy-migrate>=0.13.0 # Apache-2.0
 netaddr>=0.7.18 # BSD
 netifaces>=0.10.4 # MIT
-paramiko>=2.0.0 # LGPLv2.1+
+paramiko>=2.7.1 # LGPLv2.1+
 iso8601>=0.1.11 # MIT
 jsonschema>=3.2.0 # MIT
 python-cinderclient!=4.0.0,>=3.3.0 # Apache-2.0
@@ -71,4 +71,4 @@ zVMCloudConnector>=1.3.0;sys_platform!='win32'  # Apache 2.0 License
 futurist>=1.8.0 # Apache-2.0
 openstacksdk>=0.35.0 # Apache-2.0
 dataclasses>=0.7;python_version=='3.6'  # Apache 2.0 License
-PyYAML>=3.12 # MIT
+PyYAML>=3.13 # MIT
diff --git a/test-requirements.txt b/test-requirements.txt
index 6edddcbdbf07..98b2a0e2bce2 100644
--- a/test-requirements.txt
+++ b/test-requirements.txt
@@ -8,8 +8,8 @@ coverage!=4.4,>=4.0 # Apache-2.0
 ddt>=1.2.1 # MIT
 fixtures>=3.0.0 # Apache-2.0/BSD
 mock>=3.0.0 # BSD
-psycopg2>=2.7 # LGPL/ZPL
-PyMySQL>=0.7.6 # MIT License
+psycopg2>=2.8 # LGPL/ZPL
+PyMySQL>=0.8.0 # MIT License
 python-barbicanclient>=4.5.2 # Apache-2.0
 python-ironicclient>=3.0.0 # Apache-2.0
 requests-mock>=1.2.0 # Apache-2.0