diff --git a/src/acp/_cookies.py b/src/acp/_cookies.py
index a4b05d6..8bd7e6f 100644
--- a/src/acp/_cookies.py
+++ b/src/acp/_cookies.py
@@ -5,12 +5,16 @@
 ``Set-Cookie`` headers from the upgrade response and echo them back as a
 ``Cookie`` request header for the socket lifetime.
 
-This is intentionally minimal: it stores name→value pairs without attribute
-parsing (domain/path/expiry), matching the affinity-only use case in the RFD.
+This is intentionally minimal: it stores name→value pairs and only honors
+expiration attributes that remove a cookie, matching the affinity-only use case
+in the RFD.
 """
 
 from __future__ import annotations
 
+from datetime import datetime, timezone
+from email.utils import parsedate_to_datetime
+
 __all__ = ["MemoryAcpCookieStore"]
 
 
@@ -23,16 +27,23 @@ def __init__(self) -> None:
     def store_set_cookie(self, header_value: str) -> None:
         """Ingest a single ``Set-Cookie`` header value.
 
-        Only the leading ``name=value`` pair is retained; cookie attributes
-        (``; Path=/``, ``; HttpOnly`` etc.) are ignored.
+        Only the leading ``name=value`` pair is retained; most cookie attributes
+        (``; Path=/``, ``; HttpOnly`` etc.) are ignored. Expiration attributes
+        that explicitly clear a cookie (non-positive ``Max-Age`` or a past
+        ``Expires`` value) remove any stored cookie with the same name.
         """
-        first = header_value.split(";", 1)[0].strip()
+        parts = [part.strip() for part in header_value.split(";")]
+        first = parts[0]
         if not first or "=" not in first:
             return
         name, _, value = first.partition("=")
         name = name.strip()
-        if name:
-            self._cookies[name] = value.strip()
+        if not name:
+            return
+        if _is_deletion_cookie(parts[1:]):
+            self._cookies.pop(name, None)
+            return
+        self._cookies[name] = value.strip()
 
     def store_set_cookies(self, header_values: list[str]) -> None:
         """Ingest multiple ``Set-Cookie`` header values."""
@@ -51,3 +62,37 @@ def clear(self) -> None:
 
     def __len__(self) -> int:
         return len(self._cookies)
+
+
+def _is_deletion_cookie(attributes: list[str]) -> bool:
+    return _expiry_decision(attributes) is True
+
+
+def _expiry_decision(attributes: list[str]) -> bool | None:
+    """Return whether attributes expire the cookie now.
+
+    ``True`` means delete now, ``False`` means keep the cookie, and ``None``
+    means no usable expiration attribute was present. Per RFC 6265 section 5.3,
+    a valid ``Max-Age`` attribute takes precedence over ``Expires``.
+    """
+    expires_verdict: bool | None = None
+    for attribute in attributes:
+        key, separator, value = attribute.partition("=")
+        if not separator:
+            continue
+        key = key.strip().lower()
+        value = value.strip()
+        if key == "max-age":
+            try:
+                return int(value) <= 0
+            except ValueError:
+                continue
+        if key == "expires" and expires_verdict is None:
+            try:
+                expires_at = parsedate_to_datetime(value)
+            except (TypeError, ValueError):
+                continue
+            if expires_at.tzinfo is None:
+                expires_at = expires_at.replace(tzinfo=timezone.utc)
+            expires_verdict = expires_at <= datetime.now(timezone.utc)
+    return expires_verdict
diff --git a/tests/http/test_cookies.py b/tests/http/test_cookies.py
index 5bc0ae4..d62c046 100644
--- a/tests/http/test_cookies.py
+++ b/tests/http/test_cookies.py
@@ -1,5 +1,7 @@
 from __future__ import annotations
 
+import pytest
+
 from acp._cookies import MemoryAcpCookieStore
 
 
@@ -23,6 +25,34 @@ def test_later_value_overwrites_same_name() -> None:
     assert len(store) == 1
 
 
+@pytest.mark.parametrize(
+    "expiration_attribute",
+    [
+        "Max-Age=0",
+        "Max-Age=-1",
+        "Max-Age=00",
+        "Expires=Thu, 01 Jan 1970 00:00:00 GMT",
+        "Expires=Thu, 01 Jan 1970 00:00:01 GMT",
+        "Expires=Wed, 31 Dec 1969 23:59:59 GMT",
+        "Expires=Thu, 01-Jan-1970 00:00:00 GMT",
+        "Expires=Mon, 01 Jan 2024 00:00:00 GMT",
+    ],
+)
+def test_expiring_cookie_removes_stored_value(expiration_attribute: str) -> None:
+    store = MemoryAcpCookieStore()
+    store.store_set_cookie("affinity=abc123; Path=/")
+    store.store_set_cookie(f"affinity=; {expiration_attribute}; Path=/")
+    assert store.cookie_header() is None
+    assert len(store) == 0
+
+
+def test_positive_max_age_takes_precedence_over_past_expires() -> None:
+    store = MemoryAcpCookieStore()
+    store.store_set_cookie("affinity=abc123; Path=/")
+    store.store_set_cookie("affinity=keepme; Max-Age=3600; Expires=Thu, 01 Jan 1970 00:00:00 GMT")
+    assert store.cookie_header() == "affinity=keepme"
+
+
 def test_empty_store_returns_none() -> None:
     store = MemoryAcpCookieStore()
     assert store.cookie_header() is None