diff --git a/src/humanize/time.py b/src/humanize/time.py
index 7c4a28eb..a14f5250 100644
--- a/src/humanize/time.py
+++ b/src/humanize/time.py
@@ -61,10 +61,10 @@ def _abs_timedelta(delta: dt.timedelta) -> dt.timedelta:
     Returns:
         datetime.timedelta: Absolute timedelta.
     """
-    if delta.days < 0:
-        now = _now()
-        return now - (now + delta)
-    return delta
+    # Use abs() rather than round-tripping through the current datetime:
+    # `now + delta` overflows (OverflowError) when a negative delta reaches back
+    # past year 1, e.g. for naturaltime(dt.datetime(9999, 12, 31)).
+    return abs(delta)
 
 
 def _date_and_delta(
diff --git a/tests/test_time.py b/tests/test_time.py
index 887a3fc5..c483e669 100644
--- a/tests/test_time.py
+++ b/tests/test_time.py
@@ -196,6 +196,9 @@ def test_naturaldelta_too_large_value_raises() -> None:
         (NOW - dt.timedelta(days=365 + 35), "1 year, 1 month ago"),
         (dt.timedelta(days=-10000), "27 years from now"),
         (dt.timedelta(days=365 + 35), "1 year, 1 month ago"),
+        # far-future values used to raise OverflowError in _abs_timedelta
+        (dt.datetime(9999, 12, 31), "7,995 years from now"),
+        (dt.timedelta(days=-800_000), "2,192 years from now"),
         (22.5, "22 seconds ago"),
         (23.5, "24 seconds ago"),
         (23.9, "24 seconds ago"),
@@ -645,6 +648,12 @@ def test_precisedelta_one_unit_enough(
         (dt.timedelta(days=32), "seconds", "1 month and 1 day"),
         (dt.timedelta(days=62), "seconds", "2 months and 1 day"),
         (dt.timedelta(days=92), "seconds", "3 months"),
+        # a negative delta reaching back past year 1 used to raise OverflowError
+        (
+            dt.timedelta(days=-800_000),
+            "seconds",
+            "2,191 years, 9 months and 10 days",
+        ),
         (dt.timedelta(days=31), "days", "1 month"),
         (dt.timedelta(days=32), "days", "1 month and 1 day"),
         (dt.timedelta(days=62), "days", "2 months and 1 day"),