diff --git a/src/humanize/number.py b/src/humanize/number.py
index 2fb22c6..593b408 100644
--- a/src/humanize/number.py
+++ b/src/humanize/number.py
@@ -109,7 +109,8 @@ def ordinal(value: NumberOrString, gender: str = "male") -> str:
     except (TypeError, ValueError):
         return str(value)
     gender = "male" if gender == "male" else "female"
-    digit = 0 if value % 100 in (11, 12, 13) else value % 10
+    abs_value = abs(value)
+    digit = 0 if abs_value % 100 in (11, 12, 13) else abs_value % 10
     return f"{value}{P_(f'{digit} ({gender})', _ORDINAL_SUFFIXES[digit])}"
 
 
diff --git a/src/humanize/time.py b/src/humanize/time.py
index 4a07d52..41e5677 100644
--- a/src/humanize/time.py
+++ b/src/humanize/time.py
@@ -151,7 +151,7 @@ def naturaldelta(
             int(value)  # Explicitly don't support string such as "NaN" or "inf"
             value = float(value)
             delta = dt.timedelta(seconds=value)
-        except (ValueError, TypeError):
+        except (ValueError, TypeError, OverflowError):
             return str(value)
 
     use_months = months
diff --git a/tests/test_number.py b/tests/test_number.py
index 78639c3..204d172 100644
--- a/tests/test_number.py
+++ b/tests/test_number.py
@@ -25,6 +25,16 @@
         ("102", "102nd"),
         ("103", "103rd"),
         ("111", "111th"),
+        (-1, "-1st"),
+        (-2, "-2nd"),
+        (-3, "-3rd"),
+        (-4, "-4th"),
+        (-11, "-11th"),
+        (-12, "-12th"),
+        (-13, "-13th"),
+        (-21, "-21st"),
+        (-101, "-101st"),
+        (-111, "-111th"),
         ("something else", "something else"),
         (None, "None"),
         (math.nan, "NaN"),
diff --git a/tests/test_time.py b/tests/test_time.py
index 7699770..771e763 100644
--- a/tests/test_time.py
+++ b/tests/test_time.py
@@ -3,6 +3,7 @@
 from __future__ import annotations
 
 import datetime as dt
+import math
 import typing
 
 import pytest
@@ -128,6 +129,8 @@ def test_naturaldelta_nomonths(test_input: dt.timedelta, expected: str) -> None:
         (dt.timedelta(days=365), "a year"),
         (dt.timedelta(days=365 * 1_141), "1,141 years"),
         ("NaN", "NaN"),  # Returns non-numbers unchanged.
+        (float("inf"), "inf"),
+        (float("-inf"), "-inf"),
         # largest possible timedelta
         (dt.timedelta(days=999_999_999), "2,739,726 years"),
     ],
@@ -135,7 +138,8 @@ def test_naturaldelta_nomonths(test_input: dt.timedelta, expected: str) -> None:
 def test_naturaldelta(test_input: float | dt.timedelta, expected: str) -> None:
     assert humanize.naturaldelta(test_input) == expected
     if not isinstance(test_input, str):
-        assert humanize.naturaldelta(-test_input) == expected
+        if isinstance(test_input, dt.timedelta) or math.isfinite(test_input):
+            assert humanize.naturaldelta(-test_input) == expected
 
 
 @freeze_time(FROZEN_DATE)