diff --git a/markdown/htmlparser.py b/markdown/htmlparser.py
index a698814db..795e29ba1 100644
--- a/markdown/htmlparser.py
+++ b/markdown/htmlparser.py
@@ -131,6 +131,9 @@ def handle_starttag(self, tag, attrs):
             self._cache.append(text)
         else:
             self.cleandoc.append(text)
+            if tag in self.CDATA_CONTENT_ELEMENTS:
+                # This is presumably a standalone tag in a code span (see #1036).
+                self.clear_cdata_mode()
 
     def handle_endtag(self, tag):
         text = self.get_endtag_text(tag)
@@ -207,3 +210,63 @@ def handle_pi(self, data):
     def unknown_decl(self, data):
         end = ']]>' if data.startswith('CDATA[') else ']>'
         self.handle_empty_tag('<![{}{}'.format(data, end), is_block=True)
+
+    # The rest has been copied from base class in standard lib to address #1036.
+    # As __startag_text is private, all references to it must be in this subclass.
+    # The last few lines of parse_starttag are reversed so that handle_starttag
+    # can override cdata_mode in certain situations (in a code span).
+        __starttag_text = None
+
+    def get_starttag_text(self):
+        """Return full source of start tag: '<...>'."""
+        return self.__starttag_text
+        
+    def parse_starttag(self, i):
+        self.__starttag_text = None
+        endpos = self.check_for_whole_start_tag(i)
+        if endpos < 0:
+            return endpos
+        rawdata = self.rawdata
+        self.__starttag_text = rawdata[i:endpos]
+
+        # Now parse the data between i+1 and j into a tag and attrs
+        attrs = []
+        match = htmlparser.tagfind_tolerant.match(rawdata, i+1)
+        assert match, 'unexpected call to parse_starttag()'
+        k = match.end()
+        self.lasttag = tag = match.group(1).lower()
+        while k < endpos:
+            m = htmlparser.attrfind_tolerant.match(rawdata, k)
+            if not m:
+                break
+            attrname, rest, attrvalue = m.group(1, 2, 3)
+            if not rest:
+                attrvalue = None
+            elif attrvalue[:1] == '\'' == attrvalue[-1:] or \
+                 attrvalue[:1] == '"' == attrvalue[-1:]:
+                attrvalue = attrvalue[1:-1]
+            if attrvalue:
+                attrvalue = htmlparser.unescape(attrvalue)
+            attrs.append((attrname.lower(), attrvalue))
+            k = m.end()
+
+        end = rawdata[k:endpos].strip()
+        if end not in (">", "/>"):
+            lineno, offset = self.getpos()
+            if "\n" in self.__starttag_text:
+                lineno = lineno + self.__starttag_text.count("\n")
+                offset = len(self.__starttag_text) \
+                         - self.__starttag_text.rfind("\n")
+            else:
+                offset = offset + len(self.__starttag_text)
+            self.handle_data(rawdata[i:endpos])
+            return endpos
+        if end.endswith('/>'):
+            # XHTML-style empty tag: <span attr="value" />
+            self.handle_startendtag(tag, attrs)
+        else:
+            # *** set cdata_mode first so we can override it in handle_starttag (see #1036) ***
+            if tag in self.CDATA_CONTENT_ELEMENTS:
+                self.set_cdata_mode(tag)
+            self.handle_starttag(tag, attrs)
+        return endpos
diff --git a/tests/test_syntax/blocks/test_html_blocks.py b/tests/test_syntax/blocks/test_html_blocks.py
index 11884e186..3b4ad3643 100644
--- a/tests/test_syntax/blocks/test_html_blocks.py
+++ b/tests/test_syntax/blocks/test_html_blocks.py
@@ -1363,4 +1363,42 @@ def test_unclosed_script_tag(self):
                 Still part of the *script* tag
                 """
             )
+        )
+    
+    def test_inline_script_tags(self):
+        # Ensure inline script tags doesn't cause the parser to eat content (see #1036).
+        self.assertMarkdownRenders(
+            self.dedent(
+                """
+                Text `<script>` more *text*.
+                
+                <div>
+                *foo*
+                </div>
+
+                <div>
+
+                bar
+
+                </div>
+                                
+                A new paragraph with a closing `</script>` tag.
+                """
+            ),
+            self.dedent(
+                """
+                <p>Text <code>&lt;script&gt;</code> more <em>text</em>.</p>
+                <div>
+                *foo*
+                </div>
+
+                <div>
+
+                bar
+
+                </div>
+                
+                <p>A new paragraph with a closing <code>&lt;/script&gt;</code> tag.</p>
+                """
+            )
         )
\ No newline at end of file