diff --git a/.travis.yml b/.travis.yml
index 29f1d441..ad97b4a1 100644
--- a/.travis.yml
+++ b/.travis.yml
@@ -7,7 +7,9 @@ python:
   - 3.6
   - nightly
   - pypy
-  - pypy-5.3
+  - pypy3.5-5.8.0
+  - pypy3.5-5.9.0
+  - pypy3.5-5.10.1
   - pypy3
 install:
   - pip install --upgrade .
diff --git a/pyflakes/checker.py b/pyflakes/checker.py
index 1c30dda5..b820ffff 100644
--- a/pyflakes/checker.py
+++ b/pyflakes/checker.py
@@ -13,9 +13,10 @@
 PY2 = sys.version_info < (3, 0)
 PY34 = sys.version_info < (3, 5)    # Python 2.7 to 3.4
 try:
-    sys.pypy_version_info
+    PYPY_VERSION = sys.pypy_version_info
     PYPY = True
 except AttributeError:
+    PYPY_VERSION = None
     PYPY = False
 
 builtin_vars = dir(__import__('__builtin__' if PY2 else 'builtins'))
@@ -951,7 +952,7 @@ def handleDoctests(self, node):
                 tree = compile(example.source, "<doctest>", "exec", ast.PyCF_ONLY_AST)
             except SyntaxError:
                 e = sys.exc_info()[1]
-                if PYPY:
+                if PYPY and PYPY_VERSION < (6, ):
                     e.offset += 1
                 position = (node_lineno + example.lineno + e.lineno,
                             example.indent + 4 + (e.offset or 0))
diff --git a/pyflakes/test/test_api.py b/pyflakes/test/test_api.py
index 56ca269a..b833674f 100644
--- a/pyflakes/test/test_api.py
+++ b/pyflakes/test/test_api.py
@@ -26,9 +26,10 @@
     unichr = chr
 
 try:
-    sys.pypy_version_info
+    PYPY_VERSION = sys.pypy_version_info
     PYPY = True
 except AttributeError:
+    PYPY_VERSION = None
     PYPY = False
 
 try:
@@ -483,6 +484,10 @@ def foo(bar=baz, bax):
         sourcePath = self.makeTempFile(source)
         last_line = '       ^\n' if ERROR_HAS_LAST_LINE else ''
         column = '8:' if ERROR_HAS_COL_NUM else ''
+        if PYPY and PYPY_VERSION >= (5, 10):
+            column = '7:'
+            last_line = last_line[1:]
+
         self.assertHasErrors(
             sourcePath,
             ["""\
@@ -502,6 +507,9 @@ def test_nonKeywordAfterKeywordSyntaxError(self):
         sourcePath = self.makeTempFile(source)
         last_line = '            ^\n' if ERROR_HAS_LAST_LINE else ''
         column = '13:' if ERROR_HAS_COL_NUM or PYPY else ''
+        if PYPY and PYPY_VERSION >= (5, 10):
+            column = '12:'
+            last_line = last_line[1:]
 
         if sys.version_info >= (3, 5):
             message = 'positional argument follows keyword argument'