diff --git a/src/packaging/version.py b/src/packaging/version.py
index a11d4639..936dc7e6 100644
--- a/src/packaging/version.py
+++ b/src/packaging/version.py
@@ -548,6 +548,175 @@ def _key(self) -> CmpKey:
             )
         return self._key_cache
 
+    # __hash__ must be defined when __eq__ is overridden,
+    # otherwise Python sets __hash__ to None.
+    def __hash__(self) -> int:
+        return hash(self._key)
+
+    # Override comparison methods to use direct _key_cache access
+    # This is faster than property access, especially before Python 3.12
+    def __lt__(self, other: _BaseVersion) -> bool:
+        if isinstance(other, Version):
+            if self._key_cache is None:
+                self._key_cache = _cmpkey(
+                    self._epoch,
+                    self._release,
+                    self._pre,
+                    self._post,
+                    self._dev,
+                    self._local,
+                )
+            if other._key_cache is None:
+                other._key_cache = _cmpkey(
+                    other._epoch,
+                    other._release,
+                    other._pre,
+                    other._post,
+                    other._dev,
+                    other._local,
+                )
+            return self._key_cache < other._key_cache
+
+        if not isinstance(other, _BaseVersion):
+            return NotImplemented
+
+        return super().__lt__(other)
+
+    def __le__(self, other: _BaseVersion) -> bool:
+        if isinstance(other, Version):
+            if self._key_cache is None:
+                self._key_cache = _cmpkey(
+                    self._epoch,
+                    self._release,
+                    self._pre,
+                    self._post,
+                    self._dev,
+                    self._local,
+                )
+            if other._key_cache is None:
+                other._key_cache = _cmpkey(
+                    other._epoch,
+                    other._release,
+                    other._pre,
+                    other._post,
+                    other._dev,
+                    other._local,
+                )
+            return self._key_cache <= other._key_cache
+
+        if not isinstance(other, _BaseVersion):
+            return NotImplemented
+
+        return super().__le__(other)
+
+    def __eq__(self, other: object) -> bool:
+        if isinstance(other, Version):
+            if self._key_cache is None:
+                self._key_cache = _cmpkey(
+                    self._epoch,
+                    self._release,
+                    self._pre,
+                    self._post,
+                    self._dev,
+                    self._local,
+                )
+            if other._key_cache is None:
+                other._key_cache = _cmpkey(
+                    other._epoch,
+                    other._release,
+                    other._pre,
+                    other._post,
+                    other._dev,
+                    other._local,
+                )
+            return self._key_cache == other._key_cache
+
+        if not isinstance(other, _BaseVersion):
+            return NotImplemented
+
+        return super().__eq__(other)
+
+    def __ge__(self, other: _BaseVersion) -> bool:
+        if isinstance(other, Version):
+            if self._key_cache is None:
+                self._key_cache = _cmpkey(
+                    self._epoch,
+                    self._release,
+                    self._pre,
+                    self._post,
+                    self._dev,
+                    self._local,
+                )
+            if other._key_cache is None:
+                other._key_cache = _cmpkey(
+                    other._epoch,
+                    other._release,
+                    other._pre,
+                    other._post,
+                    other._dev,
+                    other._local,
+                )
+            return self._key_cache >= other._key_cache
+
+        if not isinstance(other, _BaseVersion):
+            return NotImplemented
+
+        return super().__ge__(other)
+
+    def __gt__(self, other: _BaseVersion) -> bool:
+        if isinstance(other, Version):
+            if self._key_cache is None:
+                self._key_cache = _cmpkey(
+                    self._epoch,
+                    self._release,
+                    self._pre,
+                    self._post,
+                    self._dev,
+                    self._local,
+                )
+            if other._key_cache is None:
+                other._key_cache = _cmpkey(
+                    other._epoch,
+                    other._release,
+                    other._pre,
+                    other._post,
+                    other._dev,
+                    other._local,
+                )
+            return self._key_cache > other._key_cache
+
+        if not isinstance(other, _BaseVersion):
+            return NotImplemented
+
+        return super().__gt__(other)
+
+    def __ne__(self, other: object) -> bool:
+        if isinstance(other, Version):
+            if self._key_cache is None:
+                self._key_cache = _cmpkey(
+                    self._epoch,
+                    self._release,
+                    self._pre,
+                    self._post,
+                    self._dev,
+                    self._local,
+                )
+            if other._key_cache is None:
+                other._key_cache = _cmpkey(
+                    other._epoch,
+                    other._release,
+                    other._pre,
+                    other._post,
+                    other._dev,
+                    other._local,
+                )
+            return self._key_cache != other._key_cache
+
+        if not isinstance(other, _BaseVersion):
+            return NotImplemented
+
+        return super().__ne__(other)
+
     @property
     @_deprecated("Version._version is private and will be removed soon")
     def _version(self) -> _Version:
diff --git a/tests/test_version.py b/tests/test_version.py
index 68d5dbe4..95d0aa00 100644
--- a/tests/test_version.py
+++ b/tests/test_version.py
@@ -12,7 +12,13 @@
 import pretend
 import pytest
 
-from packaging.version import InvalidVersion, Version, _VersionReplace, parse
+from packaging.version import (
+    InvalidVersion,
+    Version,
+    _BaseVersion,
+    _VersionReplace,
+    parse,
+)
 
 if typing.TYPE_CHECKING:
     from collections.abc import Callable
@@ -103,6 +109,27 @@ def test_parse_raises() -> None:
 ]
 
 
+# Simple _BaseVersion subclass for testing comparison with non-Version types
+class SimpleVersion(_BaseVersion):
+    """A simple _BaseVersion subclass for testing cross-type comparisons."""
+
+    def __init__(self, key: typing.Any) -> None:  # noqa: ANN401
+        # If key is a string, parse it as a version to create a compatible key
+        if isinstance(key, str):
+            parsed = Version(key)
+            self._key_tuple = parsed._key
+        else:
+            self._key_tuple = key
+
+    @property
+    def _key(self) -> typing.Any:  # noqa: ANN401
+        return self._key_tuple
+
+    @_key.setter
+    def _key(self, value: typing.Any) -> None:  # noqa: ANN401
+        self._key_tuple = value
+
+
 class TestVersion:
     @pytest.mark.parametrize("version", VERSIONS)
     def test_valid_versions(self, version: str) -> None:
@@ -800,6 +827,76 @@ def test_compare_other(self, op: str, expected: bool) -> None:
 
         assert getattr(operator, op)(Version("1"), other) is expected
 
+    @pytest.mark.parametrize(
+        "op", ["__lt__", "__le__", "__eq__", "__ge__", "__gt__", "__ne__"]
+    )
+    def test_base_version_notimplemented_with_non_base_version(self, op: str) -> None:
+        """Test _BaseVersion returns NotImplemented with non-_BaseVersion."""
+        v = SimpleVersion("1.0")
+        assert getattr(v, op)(1) is NotImplemented
+
+    def test_base_version_hash(self) -> None:
+        """Test that _BaseVersion hash works"""
+        v = SimpleVersion("1.0")
+        assert isinstance(hash(v), int)
+
+    def test_base_version_ne_with_base_version(self) -> None:
+        """Test _BaseVersion.__ne__ with another _BaseVersion."""
+        v1 = SimpleVersion("1.0")
+        v2 = SimpleVersion("2.0")
+        assert v1 != v2
+
+    def test_version_compare_with_base_version_subclass(self) -> None:
+        """Test Version comparison with another _BaseVersion subclass"""
+        v1 = Version("1.0")
+        v2 = SimpleVersion("1.0")
+
+        # All comparisons should work with compatible keys
+        assert v1 == v2
+        assert v1 <= v2
+        assert v1 >= v2
+        assert v1 == v2
+        assert not (v1 < v2)
+        assert not (v1 > v2)
+
+        # Test with different versions to exercise != path
+        v3 = Version("1.0")
+        v4 = SimpleVersion("2.0")
+        assert v3 != v4
+
+    def test_version_ne_with_uncached_keys(self) -> None:
+        """Test Version.__ne__ populates cache when comparing with another Version"""
+        v1 = Version("1.0")
+        v2 = Version("2.0")
+
+        # Test with both caches None
+        result = v1 != v2
+        assert result is True
+
+        # Test with v1 cached, v3 uncached
+        v3 = Version("1.5")
+        result = v1 != v3
+        assert result is True
+
+        # Test with v3 cached, v4 uncached (the reverse case)
+        v4 = Version("1.2")
+        result = v4 != v3
+        assert result is True
+
+    def test_version_le_with_uncached_keys(self) -> None:
+        """Test Version.__le__ populates cache when comparing with another Version"""
+        v1 = Version("1.0")
+        v2 = Version("2.0")
+
+        # Test <= with both caches None
+        result = v1 <= v2
+        assert result is True
+
+        # Test with v1 cached (from above), v3 uncached
+        v3 = Version("1.5")
+        result = v1 <= v3
+        assert result is True
+
     def test_major_version(self) -> None:
         assert Version("2.1.0").major == 2