diff --git a/changelog.d/pr494.bugfix.rst b/changelog.d/pr494.bugfix.rst
new file mode 100644
index 0000000..153f804
--- /dev/null
+++ b/changelog.d/pr494.bugfix.rst
@@ -0,0 +1,2 @@
+Bumping numeric prerelease and build identifiers now works when an identifier
+exceeds Python's integer string conversion limit.
diff --git a/src/semver/version.py b/src/semver/version.py
index 7ead382..c99542a 100644
--- a/src/semver/version.py
+++ b/src/semver/version.py
@@ -293,6 +293,20 @@ def __iter__(self) -> VersionIterator:
         """Return iter(self)."""
         yield from self.to_tuple()
 
+    @staticmethod
+    def _increment_number(number: str) -> str:
+        """Increment an ASCII decimal string without a size limit."""
+        if not number.isascii():
+            return str(int(number) + 1)
+
+        number = number.lstrip("0")
+        prefix = number.rstrip("9")
+        if prefix:
+            return prefix[:-1] + str(int(prefix[-1]) + 1) + "0" * (
+                len(number) - len(prefix)
+            )
+        return "1" + "0" * len(number)
+
     @staticmethod
     def _increment_prerelease(string: str) -> str:
         """
@@ -304,7 +318,7 @@ def _increment_prerelease(string: str) -> str:
         """
         match = Version._LAST_PRERELEASE.search(string)
         if match:
-            next_ = str(int(match.group(2)) + 1)
+            next_ = Version._increment_number(match.group(2))
             string = match.group(1) + next_ if match.group(1) else next_
         else:
             string += ".0"
@@ -323,7 +337,7 @@ def _increment_string(string: str) -> str:
         """
         match = Version._LAST_NUMBER.search(string)
         if match:
-            next_ = str(int(match.group(1)) + 1)
+            next_ = Version._increment_number(match.group(1))
             start, end = match.span(1)
             string = string[: max(end - len(next_), start)] + next_ + string[end:]
         return string
@@ -553,9 +567,9 @@ def next_version(self, part: str, prerelease_token: str = "rc") -> "Version":
                     rf"{re.escape(prerelease_token)}(\d+)", version.prerelease
                 )
                 if match:
-                    num = int(match.group(1))
+                    num = cls._increment_number(match.group(1))
                     return version.replace(
-                        prerelease=f"{prerelease_token}{num + 1}", build=None
+                        prerelease=f"{prerelease_token}{num}", build=None
                     )
 
                 if not (
diff --git a/tests/test_bump_large_identifiers.py b/tests/test_bump_large_identifiers.py
new file mode 100644
index 0000000..d2f0d3c
--- /dev/null
+++ b/tests/test_bump_large_identifiers.py
@@ -0,0 +1,46 @@
+import pytest
+
+from semver import Version
+
+
+@pytest.mark.parametrize(
+    "number,expected",
+    [
+        ("1" * 5000, "1" * 4999 + "2"),
+        ("9" * 5000, "1" + "0" * 5000),
+        ("1" + "9" * 4999, "2" + "0" * 4999),
+    ],
+    ids=["no-carry", "new-digit", "carry"],
+)
+@pytest.mark.parametrize("part", ["prerelease", "build", "old-style-prerelease"])
+def test_bump_large_numeric_identifier(number, expected, part):
+    if part == "build":
+        original = "1.2.3-rc.1+build." + number + ".tail"
+        version = Version.parse(original)
+        result = version.bump_build()
+        expected_version = "1.2.3-rc.1+build." + expected + ".tail"
+    elif part == "old-style-prerelease":
+        original = "1.2.3-rc" + number + "+build.1"
+        version = Version.parse(original)
+        result = version.next_version("prerelease", "rc")
+        expected_version = "1.2.3-rc" + expected
+    else:
+        original = "1.2.3-rc." + number + "+build.1"
+        version = Version.parse(original)
+        result = version.bump_prerelease()
+        expected_version = "1.2.3-rc." + expected
+
+    assert str(result) == expected_version
+    assert Version.is_valid(str(result))
+    assert str(version) == original
+
+
+def test_bump_preserves_constructor_unicode_digit_behavior():
+    version = Version(1, 2, 3, prerelease="rc.\u0660\u0660\u0669")
+    assert version.bump_prerelease().prerelease == "rc.10"
+
+    version = Version(1, 2, 3, build="build.\u0660\u0660\u0669")
+    assert version.bump_build().build == "build.\u066010"
+
+    version = Version(1, 2, 3, prerelease="rc\u0660\u0660\u0669")
+    assert version.next_version("prerelease", "rc").prerelease == "rc10"