diff --git a/python/src/com/jetbrains/python/psi/impl/PyBuiltinCache.java b/python/src/com/jetbrains/python/psi/impl/PyBuiltinCache.java
index 8ce29a200eda..a4d3cbe76422 100644
--- a/python/src/com/jetbrains/python/psi/impl/PyBuiltinCache.java
+++ b/python/src/com/jetbrains/python/psi/impl/PyBuiltinCache.java
@@ -395,7 +395,8 @@ public class PyBuiltinCache {
     }
   }
 
-  private PyType getStrOrUnicodeType() {
+  @Nullable
+  public PyType getStrOrUnicodeType() {
     return PyUnionType.union(getObjectType("str"), getObjectType("unicode"));
   }
 
diff --git a/python/src/com/jetbrains/python/psi/types/PyTypeChecker.java b/python/src/com/jetbrains/python/psi/types/PyTypeChecker.java
index d6862d48bbaa..2a60dd6f54c4 100644
--- a/python/src/com/jetbrains/python/psi/types/PyTypeChecker.java
+++ b/python/src/com/jetbrains/python/psi/types/PyTypeChecker.java
@@ -61,6 +61,14 @@ public class PyTypeChecker {
   private static boolean match(@Nullable PyType expected, @Nullable PyType actual, @NotNull TypeEvalContext context,
                                @Nullable Map<PyGenericType, PyType> substitutions, boolean recursive) {
     // TODO: subscriptable types?, module types?, etc.
+    if (actual instanceof PyClassType) {
+      final PyClassType classType = (PyClassType)actual;
+      final PyBuiltinCache builtinCache = PyBuiltinCache.getInstance(classType.getPyClass());
+
+      if (actual == builtinCache.getObjectType(PyNames.BASESTRING)) {
+        return match(expected, builtinCache.getStrOrUnicodeType(), context, substitutions, recursive);
+      }
+    }
     if (expected instanceof PyGenericType && substitutions != null) {
       final PyGenericType generic = (PyGenericType)expected;
       final PyType subst = substitutions.get(generic);
diff --git a/python/testData/inspections/PyTypeCheckerInspection/ActualBasestringExpectedUnionStrUnicode.py b/python/testData/inspections/PyTypeCheckerInspection/ActualBasestringExpectedUnionStrUnicode.py
new file mode 100644
index 000000000000..8e1907b57b18
--- /dev/null
+++ b/python/testData/inspections/PyTypeCheckerInspection/ActualBasestringExpectedUnionStrUnicode.py
@@ -0,0 +1,5 @@
+def hello(filename):
+    """
+    :type filename: basestring
+    """
+    open(filename)
\ No newline at end of file
diff --git a/python/testSrc/com/jetbrains/python/inspections/PyTypeCheckerInspectionTest.java b/python/testSrc/com/jetbrains/python/inspections/PyTypeCheckerInspectionTest.java
index be038d980254..9508c405bd1b 100644
--- a/python/testSrc/com/jetbrains/python/inspections/PyTypeCheckerInspectionTest.java
+++ b/python/testSrc/com/jetbrains/python/inspections/PyTypeCheckerInspectionTest.java
@@ -331,4 +331,9 @@ public class PyTypeCheckerInspectionTest extends PyTestCase {
   public void testCsvRegisterDialect() {
     doMultiFileTest();
   }
+
+  // PY-20364
+  public void testActualBasestringExpectedUnionStrUnicode() {
+    doTest();
+  }
 }