diff --git a/src/humanize/time.py b/src/humanize/time.py
index 4a07d528..975cc03c 100644
--- a/src/humanize/time.py
+++ b/src/humanize/time.py
@@ -153,6 +153,16 @@ def naturaldelta(
             delta = dt.timedelta(seconds=value)
         except (ValueError, TypeError):
             return str(value)
+        except OverflowError:
+            # `int(value)` raises OverflowError for non-finite floats (inf/-inf),
+            # which, like NaN, are returned unchanged. A too-large *finite* value
+            # (whose OverflowError comes from `timedelta`) is still raised, per
+            # the documented `OverflowError` contract.
+            import math
+
+            if not math.isfinite(value):
+                return str(value)
+            raise
 
     use_months = months
 
diff --git a/tests/test_time.py b/tests/test_time.py
index 76997704..c3743bbc 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
 
 
+@pytest.mark.parametrize(
+    "value, expected",
+    [
+        (float("nan"), "nan"),
+        (float("inf"), "inf"),
+        (float("-inf"), "-inf"),
+    ],
+)
+def test_naturaldelta_non_finite(value: float, expected: str) -> None:
+    """Non-finite floats are returned unchanged instead of raising."""
+    assert humanize.naturaldelta(value) == expected
+
+
+def test_naturaldelta_too_large_value_raises() -> None:
+    """A too-large *finite* value still raises OverflowError (unlike inf)."""
+    with pytest.raises(OverflowError):
+        humanize.naturaldelta(1e30)
+
+
 @freeze_time(FROZEN_DATE)
 @pytest.mark.parametrize(
     "test_input, expected",