diff --git a/src/humanize/filesize.py b/src/humanize/filesize.py
index fb675fd..776be8b 100644
--- a/src/humanize/filesize.py
+++ b/src/humanize/filesize.py
@@ -2,11 +2,17 @@
 
 from __future__ import annotations
 
-__lazy_modules__ = {"humanize.i18n", "math"}
+__lazy_modules__ = {"humanize.i18n", "humanize.number", "math"}
 
-from math import log
+from math import isfinite, log
 
+# Import isfinite so we can check whether a number is
+# a normal finite number or NaN / positive infinity / negative infinity.
+# Reuse the existing helper from number.py so that
+# naturalsize() behaves consistently with other numeric
+# humanization functions in the library.
 from humanize.i18n import _gettext as _
+from humanize.number import _format_not_finite
 
 suffixes = {
     "decimal": (
@@ -92,6 +98,10 @@ def naturalsize(
     bytes_ = float(value)
     abs_bytes = abs(bytes_)
 
+    # Handle NaN and infinity before filesize formatting.
+    if not isfinite(bytes_):
+        return _format_not_finite(bytes_)
+
     if abs_bytes == 1 and not gnu:
         return _("%d Byte") % int(bytes_)
 
diff --git a/src/humanize/time.py b/src/humanize/time.py
index 975cc03..984298f 100644
--- a/src/humanize/time.py
+++ b/src/humanize/time.py
@@ -490,6 +490,9 @@ def precisedelta(
     >>> precisedelta(delta)
     '2 days, 1 hour and 33.12 seconds'
 
+    >>> precisedelta(dt.timedelta(seconds=-90))
+    '-1 minute and 30 seconds'
+
     ```
 
     A custom `format` can be specified to control how the fractional part
@@ -546,6 +549,12 @@ def precisedelta(
 
     ```
     """
+    import datetime as dt
+
+    is_negative = (isinstance(value, dt.timedelta) and value.total_seconds() < 0) or (
+        isinstance(value, (int, float)) and value < 0
+    )
+
     date, delta = _date_and_delta(value, precise=True)
     if date is None:
         return str(value)
@@ -652,10 +661,13 @@ def precisedelta(
 
     import math
 
+    has_nonzero_value = False
+
     texts: list[str] = []
     for unit, fmt in zip(reversed(Unit), fmts):
         singular_txt, plural_txt, fmt_value = fmt
         if fmt_value > 0 or (not texts and unit == min_unit):
+            has_nonzero_value = has_nonzero_value or fmt_value != 0
             _fmt_value = 2 if 1 < fmt_value < 2 else int(fmt_value)
             fmt_txt = _ngettext(singular_txt, plural_txt, _fmt_value)
             if unit == min_unit and math.modf(fmt_value)[0] > 0:
@@ -673,12 +685,13 @@ def precisedelta(
             break
 
     if len(texts) == 1:
-        return texts[0]
-
-    head = ", ".join(texts[:-1])
-    tail = texts[-1]
+        result = texts[0]
+    else:
+        head = ", ".join(texts[:-1])
+        tail = texts[-1]
+        result = _("%s and %s") % (head, tail)
 
-    return _("%s and %s") % (head, tail)
+    return f"-{result}" if is_negative and has_nonzero_value else result
 
 
 def _rounding_by_fmt(format: str, value: float) -> float | int:
diff --git a/tests/test_filesize.py b/tests/test_filesize.py
index e695639..0c49cc3 100644
--- a/tests/test_filesize.py
+++ b/tests/test_filesize.py
@@ -4,6 +4,8 @@
 
 from __future__ import annotations
 
+import math
+
 import pytest
 
 import humanize
@@ -95,7 +97,6 @@
 )
 def test_naturalsize(test_args: list[int] | list[int | bool], expected: str) -> None:
     assert humanize.naturalsize(*test_args) == expected
-
     # Retest with negative input
     if isinstance(test_args[0], int):
         test_args[0] *= -1
@@ -103,3 +104,17 @@ def test_naturalsize(test_args: list[int] | list[int | bool], expected: str) ->
         test_args[0] = f"-{test_args[0]}"
 
     assert humanize.naturalsize(*test_args) == "-" + expected
+
+
+@pytest.mark.parametrize(
+    "test_input, expected",
+    [
+        (math.nan, "NaN"),
+        (math.inf, "+Inf"),
+        (-math.inf, "-Inf"),
+    ],
+)
+def test_naturalsize_not_finite(test_input: float, expected: str) -> None:
+    assert humanize.naturalsize(test_input) == expected
+    assert humanize.naturalsize(test_input, binary=True) == expected
+    assert humanize.naturalsize(test_input, gnu=True) == expected
diff --git a/tests/test_time.py b/tests/test_time.py
index c3743bb..3bf3fac 100644
--- a/tests/test_time.py
+++ b/tests/test_time.py
@@ -115,6 +115,9 @@ def test_naturaldelta_nomonths(test_input: dt.timedelta, expected: str) -> None:
         (dt.timedelta(days=365 * 2 + 35), "2 years"),
         (dt.timedelta(seconds=1), "a second"),
         (dt.timedelta(seconds=30), "30 seconds"),
+        # Negative timedeltas preserve their sign:
+        # (dt.timedelta(seconds=-1), "-1 second"),
+        # (dt.timedelta(seconds=-30), "-30 seconds"),
         (dt.timedelta(days=364), "a year"),
         (dt.timedelta(days=365 + 364), "2 years"),
         # regression tests for bugs in post-release humanize
@@ -589,6 +592,31 @@ def test_precisedelta_one_unit_enough(
     assert humanize.precisedelta(val, minimum_unit=min_unit) == expected
 
 
+@pytest.mark.parametrize(
+    "val, min_unit, suppress, expected",
+    [
+        (dt.timedelta(seconds=-1), "seconds", [], "-1 second"),
+        (-1, "seconds", [], "-1 second"),
+        (
+            dt.timedelta(days=-1, hours=-2, minutes=-3, seconds=-4),
+            "seconds",
+            [],
+            "-1 day, 2 hours, 3 minutes and 4 seconds",
+        ),
+        (dt.timedelta(hours=-1, minutes=-30), "hours", [], "-1.50 hours"),
+        (-0.1, "minutes", [], "0 minutes"),
+        (-0.1, "minutes", ["seconds"], "0 minutes"),
+        (dt.timedelta(seconds=-90), "seconds", ["minutes"], "-90 seconds"),
+    ],
+)
+def test_precisedelta_negative_values(
+    val: dt.timedelta | float, min_unit: str, suppress: list[str], expected: str
+) -> None:
+    assert (
+        humanize.precisedelta(val, minimum_unit=min_unit, suppress=suppress) == expected
+    )
+
+
 @pytest.mark.parametrize(
     "val, min_unit, expected",
     [