diff --git a/django/test/html.py b/django/test/html.py
index 36b44b0466..3b04217822 100644
--- a/django/test/html.py
+++ b/django/test/html.py
@@ -86,6 +86,7 @@ class Element:
             if self.children == element.children:
                 return 1
         i = 0
+        elem_child_idx = 0
         for child in self.children:
             # child is text content and element is also text content, then
             # make a simple "text" in "text"
@@ -96,9 +97,26 @@ class Element:
                     elif element in child:
                         return 1
             else:
+                # Look for element wholly within this child.
                 i += child._count(element, count=count)
                 if not count and i:
                     return i
+                # Also look for a sequence of element's children among self's
+                # children. self.children == element.children is tested above,
+                # but will fail if self has additional children. Ex: '<a/><b/>'
+                # is contained in '<a/><b/><c/>'.
+                if isinstance(element, RootElement) and element.children:
+                    elem_child = element.children[elem_child_idx]
+                    # Start or continue match, advance index.
+                    if elem_child == child:
+                        elem_child_idx += 1
+                        # Match found, reset index.
+                        if elem_child_idx == len(element.children):
+                            i += 1
+                            elem_child_idx = 0
+                    # No match, reset index.
+                    else:
+                        elem_child_idx = 0
         return i
 
     def __contains__(self, element):
diff --git a/tests/test_utils/tests.py b/tests/test_utils/tests.py
index 87e2f56979..51e3c0548a 100644
--- a/tests/test_utils/tests.py
+++ b/tests/test_utils/tests.py
@@ -768,11 +768,30 @@ class HTMLEqualTests(SimpleTestCase):
         dom2 = parse_html('<p>foo<p>bar</p></p>')
         self.assertEqual(dom2.count(dom1), 0)
 
-        # html with a root element contains the same html with no root element
+        # HTML with a root element contains the same HTML with no root element.
         dom1 = parse_html('<p>foo</p><p>bar</p>')
         dom2 = parse_html('<div><p>foo</p><p>bar</p></div>')
         self.assertEqual(dom2.count(dom1), 1)
 
+        # Target of search is a sequence of child elements and appears more
+        # than once.
+        dom2 = parse_html('<div><p>foo</p><p>bar</p><p>foo</p><p>bar</p></div>')
+        self.assertEqual(dom2.count(dom1), 2)
+
+        # Searched HTML has additional children.
+        dom1 = parse_html('<a/><b/>')
+        dom2 = parse_html('<a/><b/><c/>')
+        self.assertEqual(dom2.count(dom1), 1)
+
+        # No match found in children.
+        dom1 = parse_html('<b/><a/>')
+        self.assertEqual(dom2.count(dom1), 0)
+
+        # Target of search found among children and grandchildren.
+        dom1 = parse_html('<b/><b/>')
+        dom2 = parse_html('<a><b/><b/></a><b/><b/>')
+        self.assertEqual(dom2.count(dom1), 2)
+
     def test_parsing_errors(self):
         with self.assertRaises(AssertionError):
             self.assertHTMLEqual('<p>', '')