diff --git a/src/humanize/time.py b/src/humanize/time.py
index 4a07d52..3d5ef12 100644
--- a/src/humanize/time.py
+++ b/src/humanize/time.py
@@ -117,9 +117,6 @@ def naturaldelta(
             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.
-
     Examples:
         Compare two timestamps in a custom local timezone::
 
@@ -151,6 +148,13 @@ def naturaldelta(
             int(value)  # Explicitly don't support string such as "NaN" or "inf"
             value = float(value)
             delta = dt.timedelta(seconds=value)
+        except OverflowError:
+            # int(value) raises OverflowError for non-finite floats (inf/-inf).
+            # Like NaN they are returned unchanged. A truly too-large *finite*
+            # float still raises, preserving the documented OverflowError contract.
+            if not math.isfinite(value):
+                return str(value)
+            raise
         except (ValueError, TypeError):
             return str(value)
 
diff --git a/tests/test_time.py b/tests/test_time.py
index 7699770..d5856ed 100644
--- a/tests/test_time.py
+++ b/tests/test_time.py
@@ -138,6 +138,25 @@ def test_naturaldelta(test_input: float | dt.timedelta, expected: str) -> None:
         assert humanize.naturaldelta(-test_input) == expected
 
 
+def test_naturaldelta_non_finite_floats() -> None:
+    """Regression for #333: non-finite floats must not raise OverflowError.
+
+    float("inf") and float("-inf") trigger int(value) -> OverflowError inside
+    timedelta(seconds=value). They should be returned as strings, like float("nan").
+    A legitimately too-large *finite* float must still raise OverflowError.
+    """
+    # Non-finite values return the string repr
+    assert humanize.naturaldelta(float("inf")) == "inf"
+    assert humanize.naturaldelta(float("-inf")) == "-inf"
+    # NaN already worked before; confirm it still does
+    assert humanize.naturaldelta(float("nan")) == "nan"
+    # A truly too-large finite float must still raise (documented behaviour)
+    import pytest
+
+    with pytest.raises(OverflowError):
+        humanize.naturaldelta(1e308 * 10)
+
+
 @freeze_time(FROZEN_DATE)
 @pytest.mark.parametrize(
     "test_input, expected",