diff --git a/Lib/pyclbr.py b/Lib/pyclbr.py
--- a/Lib/pyclbr.py
+++ b/Lib/pyclbr.py
@@ -128,6 +128,8 @@
         parent = _readmodule(package, path, inpackage)
         if inpackage is not None:
             package = "%s.%s" % (inpackage, package)
+        if not '__path__' in parent:
+            raise ImportError('No package {}'.format(package), name=package)
         return _readmodule(submodule, parent['__path__'], package)
 
     # Search the path for the module
diff --git a/Lib/test/test_pyclbr.py b/Lib/test/test_pyclbr.py
--- a/Lib/test/test_pyclbr.py
+++ b/Lib/test/test_pyclbr.py
@@ -167,6 +167,11 @@
         cm('email.parser')
         cm('test.test_pyclbr')
 
+    def test_issue_XXX(self):
+        # test ImportError is raised when the first part of a dotted name is
+        # not a package
+        self.assertRaises(ImportError, pyclbr.readmodule_ex, 'asyncore.foo')
+
 
 def test_main():
     run_unittest(PyclbrTest)