diff --git a/Lib/HTMLParser.py b/Lib/HTMLParser.py
index 1c6989e7d44..516bc701470 100644
--- a/Lib/HTMLParser.py
+++ b/Lib/HTMLParser.py
@@ -160,7 +160,7 @@ class HTMLParser(markupbase.ParserBase):
                 elif startswith("<?", i):
                     k = self.parse_pi(i)
                 elif startswith("<!", i):
-                    k = self.parse_declaration(i)
+                    k = self.parse_html_declaration(i)
                 elif (i + 1) < n:
                     self.handle_data("<")
                     k = i + 1
@@ -218,6 +218,40 @@ class HTMLParser(markupbase.ParserBase):
             i = self.updatepos(i, n)
         self.rawdata = rawdata[i:]
 
+    # Internal -- parse html declarations, return length or -1 if not terminated
+    # See w3.org/TR/html5/tokenization.html#markup-declaration-open-state
+    # See also parse_declaration in _markupbase
+    def parse_html_declaration(self, i):
+        rawdata = self.rawdata
+        if rawdata[i:i+2] != '<!':
+            self.error('unexpected call to parse_html_declaration()')
+        if rawdata[i:i+4] == '<!--':
+            return self.parse_comment(i)
+        elif rawdata[i:i+3] == '<![':
+            return self.parse_marked_section(i)
+        elif rawdata[i:i+9].lower() == '<!doctype':
+            # find the closing >
+            gtpos = rawdata.find('>', 9)
+            if gtpos == -1:
+                return -1
+            self.handle_decl(rawdata[i+2:gtpos])
+            return gtpos+1
+        else:
+            return self.parse_bogus_comment(i)
+
+    # Internal -- parse bogus comment, return length or -1 if not terminated
+    # see http://www.w3.org/TR/html5/tokenization.html#bogus-comment-state
+    def parse_bogus_comment(self, i, report=1):
+        rawdata = self.rawdata
+        if rawdata[i:i+2] != '<!':
+            self.error('unexpected call to parse_comment()')
+        pos = rawdata.find('>', i+2)
+        if pos == -1:
+            return -1
+        if report:
+            self.handle_comment(rawdata[i+2:pos])
+        return pos + 1
+
     # Internal -- parse processing instr, return end or -1 if not terminated
     def parse_pi(self, i):
         rawdata = self.rawdata
diff --git a/Lib/test/test_htmlparser.py b/Lib/test/test_htmlparser.py
index 14ed80c5d09..29a721cf451 100644
--- a/Lib/test/test_htmlparser.py
+++ b/Lib/test/test_htmlparser.py
@@ -114,7 +114,7 @@ comment1b-->
 <Img sRc='Bar' isMAP>sample
 text
 &#x201C;
-<!--comment2a-- --comment2b--><!>
+<!--comment2a-- --comment2b-->
 </Html>
 """, [
     ("data", "\n"),
@@ -142,24 +142,6 @@ text
             ("data", " foo"),
             ])
 
-    def test_doctype_decl(self):
-        inside = """\
-DOCTYPE html [
-  <!ELEMENT html - O EMPTY>
-  <!ATTLIST html
-      version CDATA #IMPLIED
-      profile CDATA 'DublinCore'>
-  <!NOTATION datatype SYSTEM 'http://xml.python.org/notations/python-module'>
-  <!ENTITY myEntity 'internal parsed entity'>
-  <!ENTITY anEntity SYSTEM 'http://xml.python.org/entities/something.xml'>
-  <!ENTITY % paramEntity 'name|name|name'>
-  %paramEntity;
-  <!-- comment -->
-]"""
-        self._run_check("<!%s>" % inside, [
-            ("decl", inside),
-            ])
-
     def test_bad_nesting(self):
         # Strangely, this *is* supposed to test that overlapping
         # elements are allowed.  HTMLParser is more geared toward
@@ -182,7 +164,8 @@ DOCTYPE html [
             ])
 
     def test_illegal_declarations(self):
-        self._parse_error('<!spacer type="block" height="25">')
+        self._run_check('<!spacer type="block" height="25">',
+                        [('comment', 'spacer type="block" height="25"')])
 
     def test_starttag_end_boundary(self):
         self._run_check("""<a b='<'>""", [("starttag", "a", [("b", "<")])])
@@ -233,7 +216,7 @@ DOCTYPE html [
         self._parse_error("<a foo='>")
 
     def test_declaration_junk_chars(self):
-        self._parse_error("<!DOCTYPE foo $ >")
+        self._run_check("<!DOCTYPE foo $ >", [('decl', 'DOCTYPE foo $ ')])
 
     def test_startendtag(self):
         self._run_check("<p/>", [
@@ -449,6 +432,39 @@ class AttributesTestCase(TestCaseBase):
                           [("href", "http://www.example.org/\">;")]),
                          ("data", "spam"), ("endtag", "a")])
 
+    def test_comments(self):
+        html = ("<!-- I'm a valid comment -->"
+                '<!--me too!-->'
+                '<!------>'
+                '<!---->'
+                '<!----I have many hyphens---->'
+                '<!-- I have a > in the middle -->'
+                '<!-- and I have -- in the middle! -->')
+        expected = [('comment', " I'm a valid comment "),
+                    ('comment', 'me too!'),
+                    ('comment', '--'),
+                    ('comment', ''),
+                    ('comment', '--I have many hyphens--'),
+                    ('comment', ' I have a > in the middle '),
+                    ('comment', ' and I have -- in the middle! ')]
+        self._run_check(html, expected)
+
+    def test_broken_comments(self):
+        html = ('<! not really a comment >'
+                '<! not a comment either -->'
+                '<! -- close enough -->'
+                '<!><!<-- this was an empty comment>'
+                '<!!! another bogus comment !!!>')
+        expected = [
+            ('comment', ' not really a comment '),
+            ('comment', ' not a comment either --'),
+            ('comment', ' -- close enough --'),
+            ('comment', ''),
+            ('comment', '<-- this was an empty comment'),
+            ('comment', '!! another bogus comment !!!'),
+        ]
+        self._run_check(html, expected)
+
     def test_condcoms(self):
         html = ('<!--[if IE & !(lte IE 8)]>aren\'t<![endif]-->'
                 '<!--[if IE 8]>condcoms<![endif]-->'
diff --git a/Misc/NEWS b/Misc/NEWS
index 33189131bda..55b19b12cc4 100644
--- a/Misc/NEWS
+++ b/Misc/NEWS
@@ -90,6 +90,8 @@ Core and Builtins
 Library
 -------
 
+- Issue #13960: HTMLParser is now able to handle broken comments.
+
 - Issue #9750: Fix sqlite3.Connection.iterdump on tables and fields
   with a name that is a keyword or contains quotes. Patch by Marko
   Kohtala.