diff --git a/Lib/doctest.py b/Lib/doctest.py
index 4735b59852685c..ed94d15c0e2da4 100644
--- a/Lib/doctest.py
+++ b/Lib/doctest.py
@@ -2171,6 +2171,7 @@ def __init__(self, test, optionflags=0, setUp=None, tearDown=None,
         unittest.TestCase.__init__(self)
         self._dt_optionflags = optionflags
         self._dt_checker = checker
+        self._dt_globs = test.globs.copy()
         self._dt_test = test
         self._dt_setUp = setUp
         self._dt_tearDown = tearDown
@@ -2187,7 +2188,9 @@ def tearDown(self):
         if self._dt_tearDown is not None:
             self._dt_tearDown(test)
 
+        # restore the original globs
         test.globs.clear()
+        test.globs.update(self._dt_globs)
 
     def runTest(self):
         test = self._dt_test
diff --git a/Lib/test/test_doctest.py b/Lib/test/test_doctest.py
index 407a14c7ddf67e..35444148a522d1 100644
--- a/Lib/test/test_doctest.py
+++ b/Lib/test/test_doctest.py
@@ -3130,6 +3130,22 @@ def test_no_trailing_whitespace_stripping():
     """
 
 
+def test_run_doctestsuite_multiple_times():
+    """
+    It was not possible to run the same DocTestSuite multiple times
+    http://bugs.python.org/issue2604
+    http://bugs.python.org/issue9736
+
+    >>> import unittest
+    >>> import test.sample_doctest
+    >>> suite = doctest.DocTestSuite(test.sample_doctest)
+    >>> suite.run(unittest.TestResult())
+    <unittest.result.TestResult run=9 errors=0 failures=4>
+    >>> suite.run(unittest.TestResult())
+    <unittest.result.TestResult run=9 errors=0 failures=4>
+    """
+
+
 def load_tests(loader, tests, pattern):
     tests.addTest(doctest.DocTestSuite(doctest))
     tests.addTest(doctest.DocTestSuite())
diff --git a/Misc/NEWS.d/next/Library/2022-03-16-18-25-19.bpo-2604.jeopdL.rst b/Misc/NEWS.d/next/Library/2022-03-16-18-25-19.bpo-2604.jeopdL.rst
new file mode 100644
index 00000000000000..c0fd000b2c6604
--- /dev/null
+++ b/Misc/NEWS.d/next/Library/2022-03-16-18-25-19.bpo-2604.jeopdL.rst
@@ -0,0 +1 @@
+Fix bug where doctests using globals would fail when run multiple times.