diff --git a/src/humanize/time.py b/src/humanize/time.py
index 4a07d52..37f930d 100644
--- a/src/humanize/time.py
+++ b/src/humanize/time.py
@@ -89,7 +89,7 @@ def _date_and_delta(
             value = value if precise else round(value)
             delta = dt.timedelta(seconds=value)
             date = now - delta
-        except (ValueError, TypeError):
+        except (ValueError, TypeError, OverflowError):
             return None, value
     return date, _abs_timedelta(delta)
 
@@ -114,11 +114,9 @@ def naturaldelta(
     Returns:
         str (str or `value`): A natural representation of the amount of time
             elapsed unless `value` is not datetime.timedelta or cannot be
-            converted to int (cannot be float due to 'inf' or 'nan').
-            In that case, a `value` is returned unchanged.
-
-    Raises:
-        OverflowError: If `value` is too large to convert to datetime.timedelta.
+            converted to int (cannot be float due to 'inf' or 'nan', or too
+            large to fit in a `datetime.timedelta`). In that case, `value` is
+            returned unchanged (via `str()`).
 
     Examples:
         Compare two timestamps in a custom local timezone::
@@ -151,7 +149,7 @@ 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_time.py b/tests/test_time.py
index 7699770..033a4e5 100644
--- a/tests/test_time.py
+++ b/tests/test_time.py
@@ -837,6 +837,45 @@ def test_time_unit() -> None:
         _ = years < "foo"
 
 
+@pytest.mark.parametrize(
+    "value, expected",
+    [
+        (float("inf"), "inf"),
+        (float("-inf"), "-inf"),
+        (float("nan"), "nan"),
+    ],
+)
+def test_naturaldelta_non_finite(value: float, expected: str) -> None:
+    # Regression test for #333: non-finite floats used to raise an uncaught
+    # OverflowError (or, for nan, were only handled when passed as a string)
+    # instead of being returned unchanged like other non-numeric input.
+    assert humanize.naturaldelta(value) == expected
+
+
+@pytest.mark.parametrize(
+    "value, expected",
+    [
+        (float("inf"), "inf"),
+        (float("-inf"), "-inf"),
+        (float("nan"), "nan"),
+    ],
+)
+def test_naturaltime_non_finite(value: float, expected: str) -> None:
+    assert humanize.naturaltime(value) == expected
+
+
+@pytest.mark.parametrize(
+    "value, expected",
+    [
+        (float("inf"), "inf"),
+        (float("-inf"), "-inf"),
+        (float("nan"), "nan"),
+    ],
+)
+def test_precisedelta_non_finite(value: float, expected: str) -> None:
+    assert humanize.precisedelta(value) == expected
+
+
 @pytest.mark.parametrize(
     "fmt, value, expected",
     [