diff --git a/stubs/jwcrypto/@tests/stubtest_allowlist.txt b/stubs/jwcrypto/@tests/stubtest_allowlist.txt
index b81e7c4baa58..253d414f8eab 100644
--- a/stubs/jwcrypto/@tests/stubtest_allowlist.txt
+++ b/stubs/jwcrypto/@tests/stubtest_allowlist.txt
@@ -1,6 +1,7 @@
 # test code does not need type hints
 jwcrypto.tests
 jwcrypto.tests-cookbook
+jwcrypto.tests_mldsa
 
 # even if the deprecated decorator is applied, the attribute is not present
 jwcrypto.jwt.JWTMissingKeyID.__deprecated__
diff --git a/stubs/jwcrypto/METADATA.toml b/stubs/jwcrypto/METADATA.toml
index 746c8c0fb382..a80bbcc56e98 100644
--- a/stubs/jwcrypto/METADATA.toml
+++ b/stubs/jwcrypto/METADATA.toml
@@ -1,3 +1,3 @@
-version = "1.5.8"
+version = "1.5.9"
 upstream-repository = "https://github.com/latchset/jwcrypto"
 dependencies = ["cryptography"]
diff --git a/stubs/jwcrypto/jwcrypto/common.pyi b/stubs/jwcrypto/jwcrypto/common.pyi
index b1361916a804..1deafd70a886 100644
--- a/stubs/jwcrypto/jwcrypto/common.pyi
+++ b/stubs/jwcrypto/jwcrypto/common.pyi
@@ -19,6 +19,9 @@ class InvalidJWAAlgorithm(JWException):
 class InvalidCEKeyLength(JWException):
     def __init__(self, expected: int, obtained: int) -> None: ...
 
+class InvalidJWEData(JWException):
+    def __init__(self, message: str | None = None, exception: BaseException | None = None) -> None: ...
+
 class InvalidJWEOperation(JWException):
     def __init__(self, message: str | None = None, exception: BaseException | None = None) -> None: ...
 
diff --git a/stubs/jwcrypto/jwcrypto/jwa.pyi b/stubs/jwcrypto/jwcrypto/jwa.pyi
index e2932812cdcc..50fdc6d1158d 100644
--- a/stubs/jwcrypto/jwcrypto/jwa.pyi
+++ b/stubs/jwcrypto/jwcrypto/jwa.pyi
@@ -1,8 +1,9 @@
 from abc import ABCMeta, abstractmethod
 from collections.abc import Mapping
-from typing import ClassVar
+from typing import ClassVar, Literal
 
 default_max_pbkdf2_iterations: int
+default_warn_deprecated_algorithms: bool
 default_enforce_hmac_key_length: bool
 
 class JWAAlgorithm(metaclass=ABCMeta):
@@ -21,6 +22,8 @@ class JWAAlgorithm(metaclass=ABCMeta):
     @property
     @abstractmethod
     def algorithm_use(self) -> str: ...
+    status: Literal["active", "deprecated", "prohibited"]
+    deprecated_by: str | None
     @property
     def input_keysize(self) -> int: ...
 
diff --git a/stubs/jwcrypto/jwcrypto/jwe.pyi b/stubs/jwcrypto/jwcrypto/jwe.pyi
index 6c22794cd5e3..6c8ba45c94e6 100644
--- a/stubs/jwcrypto/jwcrypto/jwe.pyi
+++ b/stubs/jwcrypto/jwcrypto/jwe.pyi
@@ -4,7 +4,7 @@ from typing import Any
 from typing_extensions import LiteralString, Self
 
 from jwcrypto import common
-from jwcrypto.common import JWException, JWSEHeaderParameter, JWSEHeaderRegistry
+from jwcrypto.common import JWSEHeaderParameter, JWSEHeaderRegistry
 from jwcrypto.jwk import JWK, JWKSet
 
 default_max_compressed_size: int
@@ -14,10 +14,8 @@ JWEHeaderRegistry: dict[LiteralString, JWSEHeaderParameter]
 
 default_allowed_algs: list[LiteralString]
 
-class InvalidJWEData(JWException):
-    def __init__(self, message: str | None = None, exception: BaseException | None = None) -> None: ...
-
 InvalidCEKeyLength = common.InvalidCEKeyLength
+InvalidJWEData = common.InvalidJWEData
 InvalidJWEKeyLength = common.InvalidJWEKeyLength
 InvalidJWEKeyType = common.InvalidJWEKeyType
 InvalidJWEOperation = common.InvalidJWEOperation
diff --git a/stubs/jwcrypto/jwcrypto/jwk.pyi b/stubs/jwcrypto/jwcrypto/jwk.pyi
index 5cdd0bcc45ba..3db8d2739baf 100644
--- a/stubs/jwcrypto/jwcrypto/jwk.pyi
+++ b/stubs/jwcrypto/jwcrypto/jwk.pyi
@@ -11,6 +11,14 @@ from cryptography.hazmat.primitives.asymmetric.ed25519 import (
     Ed25519PrivateKey as Ed25519PrivateKey,
     Ed25519PublicKey as Ed25519PublicKey,
 )
+from cryptography.hazmat.primitives.asymmetric.mldsa import (
+    MLDSA44PrivateKey as MLDSA44PrivateKey,
+    MLDSA44PublicKey as MLDSA44PublicKey,
+    MLDSA65PrivateKey as MLDSA65PrivateKey,
+    MLDSA65PublicKey as MLDSA65PublicKey,
+    MLDSA87PrivateKey as MLDSA87PrivateKey,
+    MLDSA87PublicKey as MLDSA87PublicKey,
+)
 from cryptography.hazmat.primitives.asymmetric.x448 import X448PrivateKey as X448PrivateKey, X448PublicKey as X448PublicKey
 from cryptography.hazmat.primitives.asymmetric.x25519 import (
     X25519PrivateKey as X25519PrivateKey,
@@ -22,11 +30,11 @@ _T = TypeVar("_T")
 
 class UnimplementedOKPCurveKey:
     @classmethod
-    def generate(cls) -> None: ...
+    def generate(cls): ...
     @classmethod
-    def from_public_bytes(cls, *args) -> None: ...
+    def from_public_bytes(cls, *args): ...
     @classmethod
-    def from_private_bytes(cls, *args) -> None: ...
+    def from_private_bytes(cls, *args): ...
 
 ImplementedOkpCurves: Sequence[str]
 priv_bytes: Callable[[bytes], X25519PrivateKey] | None
@@ -47,6 +55,20 @@ class _X448_CURVE(NamedTuple):
     pubkey: UnimplementedOKPCurveKey
     privkey: UnimplementedOKPCurveKey
 
+class UnimplementedAKPAlgorithm:
+    @classmethod
+    def generate(cls): ...
+    @classmethod
+    def from_public_bytes(cls, *args): ...
+    @classmethod
+    def from_seed_bytes(cls, *args): ...
+
+ImplementedAKPAlgorithms: Sequence[str]
+
+class _AKPAlg(NamedTuple):
+    pubkey: UnimplementedAKPAlgorithm
+    privkey: UnimplementedAKPAlgorithm
+
 _JWKKeyTypeSupported: TypeAlias = Literal["oct", "RSA", "EC", "OKP"]
 JWKTypesRegistry: dict[_JWKKeyTypeSupported, str]