diff --git a/.travis.yml b/.travis.yml
index 4847904..19c2e15 100644
--- a/.travis.yml
+++ b/.travis.yml
@@ -5,6 +5,7 @@ python:
     - 3.3
     - 3.4
     - 3.5
+    - 3.6
     - pypy
     - pypy3
 install:
diff --git a/CHANGES.rst b/CHANGES.rst
index e87ec80..b48751d 100644
--- a/CHANGES.rst
+++ b/CHANGES.rst
@@ -4,7 +4,7 @@ Changes
 4.7.0 (unreleased)
 ------------------
 
-- Nothing changed yet.
+- Add support for Python 3.6.
 
 
 4.6.0 (2016-10-20)
diff --git a/appveyor.yml b/appveyor.yml
index b1ad55b..2ca17c3 100644
--- a/appveyor.yml
+++ b/appveyor.yml
@@ -9,6 +9,8 @@ environment:
     - python : 34-x64
     - python : 35
     - python : 35-x64
+    - python : 36
+    - python : 36-x64
 
 install:
   - "SET PATH=C:\\Python%PYTHON%;c:\\Python%PYTHON%\\scripts;%PATH%"
diff --git a/setup.py b/setup.py
index 45366c6..281589e 100644
--- a/setup.py
+++ b/setup.py
@@ -82,6 +82,7 @@ def read(*rnames):
         "Programming Language :: Python :: 3.3",
         "Programming Language :: Python :: 3.4",
         "Programming Language :: Python :: 3.5",
+        "Programming Language :: Python :: 3.6",
         'Programming Language :: Python :: Implementation :: CPython',
         'Programming Language :: Python :: Implementation :: PyPy',
         "Framework :: Zope3",
diff --git a/src/zope/testing/tests.py b/src/zope/testing/tests.py
index 4965ba5..e86008b 100644
--- a/src/zope/testing/tests.py
+++ b/src/zope/testing/tests.py
@@ -31,7 +31,9 @@ def test_suite():
             'module.txt',
             # Python 3.3 changed exception messaging:
             #   https://bugs.launchpad.net/zope.testing/+bug/1055720
+            # and then Python 3.6 introduced ImportError subclasses
             checker=renormalizing.RENormalizing([
+                (re.compile('ModuleNotFoundError:'), 'ImportError:'),
                 (re.compile(
                     "No module named '?zope.testing.unlikelymodulename'?"),
                  'No module named unlikelymodulename'),
diff --git a/tox.ini b/tox.ini
index c05a82b..07401dc 100644
--- a/tox.ini
+++ b/tox.ini
@@ -1,6 +1,6 @@
 [tox]
 envlist =
-    py27,py33,py34,py35,pypy,pypy3
+    py27,py33,py34,py35,py36,pypy,pypy3
 
 [testenv]
 commands =