diff --git a/tornado/httputil.py b/tornado/httputil.py
index 4ec7b68fed..e849f0ee95 100644
--- a/tornado/httputil.py
+++ b/tornado/httputil.py
@@ -145,13 +145,31 @@ def add(self, name: str, value: str) -> None:
         """Adds a new value for the given key."""
         norm_name = _normalize_header(name)
         self._last_key = norm_name
-        if norm_name in self:
-            self._dict[norm_name] = (
-                native_str(self[norm_name]) + "," + native_str(value)
-            )
-            self._as_list[norm_name].append(value)
+
+        # Handle Content-Length specifically
+        if norm_name == 'Content-Length':
+            if not value.isdigit():
+                raise HTTPInputError("Invalid Content-Length header, must be a non-negative integer")
+            if int(value) < 0:
+                raise HTTPInputError("Invalid Content-Length header, must be a non-negative integer")
+
+            if norm_name in self._dict:
+                # Compare the existing value (which is stored as a string) to the new integer value (converted to string)
+                if self._dict[norm_name] != value:
+                    raise HTTPInputError("Conflicting Content-Length headers")
+            
+            # Store the Content-Length as a string
+            self._dict[norm_name] = value  # Overwrite the existing value as a string
+            self._as_list[norm_name] = [value]  # Reset list with the new value
+            
         else:
-            self[norm_name] = value
+            # For all other headers, append the value
+            if norm_name in self._dict:
+                self._dict[norm_name] += ',' + value  # Append with a comma
+                self._as_list[norm_name].append(value)  # Append to the list
+            else:
+                self._dict[norm_name] = value
+                self._as_list[norm_name] = [value]  # Initialize the list with the new value
 
     def get_list(self, name: str) -> List[str]:
         """Returns all values for the given header as a list."""
diff --git a/tornado/test/httputil_test.py b/tornado/test/httputil_test.py
index 75c92fffd9..c56a27122d 100644
--- a/tornado/test/httputil_test.py
+++ b/tornado/test/httputil_test.py
@@ -261,6 +261,38 @@ def test_data_after_final_boundary(self):
 
 
 class HTTPHeadersTest(unittest.TestCase):
+
+    def test_multiple_content_length_headers(self):
+        headers = HTTPHeaders()
+
+        headers.parse_line("Content-Length: 123")
+
+        headers.parse_line("Content-Length: 123")
+        self.assertEqual(headers.get("content-length"), "123")
+        with self.assertRaises(HTTPInputError):
+            headers.parse_line("Content-Length: 456")  # Should raise error
+    def test_invalid_content_length(self):
+        headers = HTTPHeaders()
+        with self.assertRaises(HTTPInputError):
+            headers.parse_line("Content-Length: abc")  # Should raise error
+
+    def test_negative_content_length(self):
+        headers = HTTPHeaders()
+        with self.assertRaises(HTTPInputError):
+            headers.parse_line("Content-Length: -123")
+
+    def test_leading_trailing_whitespace(self):
+        headers = HTTPHeaders()
+        headers.parse_line("Content-Length: 123   ")
+        self.assertEqual(headers.get('content-length'), '123')  # Should handle whitespace correctly
+
+    def test_zero_content_length(self):
+        headers = HTTPHeaders()
+        headers.parse_line("Content-Length: 0")
+        self.assertEqual(headers.get('content-length'), '0')  # Should handle zero correctly
+
+
+
     def test_multi_line(self):
         # Lines beginning with whitespace are appended to the previous line
         # with any leading whitespace replaced by a single space.