diff --git a/src/proxy/hdrs/MIME.cc b/src/proxy/hdrs/MIME.cc
index 9430385d42c..d479c6fe72e 100644
--- a/src/proxy/hdrs/MIME.cc
+++ b/src/proxy/hdrs/MIME.cc
@@ -3812,9 +3812,13 @@ MIMEHdrImpl::recompute_cooked_stuff(MIMEField *changing_field_or_null, const std
                   csv_value_mask                         = 0;
                   m_cooked_stuff.m_cache_control.m_mask &= ~mask;
                 }
+              } else if (token_wks == MIME_VALUE_MAX_STALE.c_str()) {
+                // RFC 9111, Section 5.2.1.2: a valueless max-stale request
+                // directive permits a stale response of any age.
+                m_cooked_stuff.m_cache_control.m_secs_max_stale = INT_MAX;
               } else {
-                // No '=' found, or whitespace before '='. This is malformed.
-                // For directives that require values, this is an error.
+                // No '=' found, or whitespace before '='. This is malformed
+                // for directives that require values.
                 // Clear the mask for this directive.
                 csv_value_mask                         = 0;
                 m_cooked_stuff.m_cache_control.m_mask &= ~mask;
diff --git a/src/proxy/hdrs/unit_tests/test_HdrUtils.cc b/src/proxy/hdrs/unit_tests/test_HdrUtils.cc
index befd37b5502..c6b60a87bcb 100644
--- a/src/proxy/hdrs/unit_tests/test_HdrUtils.cc
+++ b/src/proxy/hdrs/unit_tests/test_HdrUtils.cc
@@ -22,6 +22,7 @@
 #include <cstring>
 #include <cctype>
 #include <bitset>
+#include <climits>
 #include <initializer_list>
 #include <new>
 #include <vector>
@@ -426,6 +427,11 @@ TEST_CASE("Cache-Control Valid Cooking", "[proxy][hdrutils]")
      MIME_COOKED_MASK_CC_MAX_STALE,
      0, 0, 100, 0},
 
+    {"max-stale without a value",
+     "Cache-Control: max-stale\r\n\r\n",
+     MIME_COOKED_MASK_CC_MAX_STALE,
+     0, 0, INT_MAX, 0},
+
     {"min-fresh=60",
      "Cache-Control: min-fresh=60\r\n\r\n",
      MIME_COOKED_MASK_CC_MIN_FRESH,
diff --git a/tests/gold_tests/cache/replay/cache-control-basic.replay.yaml b/tests/gold_tests/cache/replay/cache-control-basic.replay.yaml
index 02a6264256f..cb6d670e124 100644
--- a/tests/gold_tests/cache/replay/cache-control-basic.replay.yaml
+++ b/tests/gold_tests/cache/replay/cache-control-basic.replay.yaml
@@ -19,7 +19,7 @@ meta:
 
 # Configuration section for autest integration
 autest:
-  description: 'Test basic cache operations: miss, hit, no-cache-control, stale, and only-if-cached'
+  description: 'Test basic cache operations: miss, hit, no-cache-control, stale, only-if-cached, and max-stale'
 
   dns:
     name: 'dns-cache-basic'
@@ -221,3 +221,74 @@ sessions:
         fields:
         - [X-Cache, { value: "miss", as: equal }]
         - [Cache-Control, { value: "no-store", as: equal }]
+
+  #############################################################################
+  # Test 6: Populate an entry for a valueless max-stale request
+  #############################################################################
+  - client-request:
+      method: GET
+      url: /max-stale
+      version: '1.1'
+      headers:
+        fields:
+        - [Host, www.example.com]
+        - [x-debug, "x-cache,x-cache-key,via"]
+        - [uuid, max-stale-populate]
+
+    server-response:
+      status: 200
+      reason: OK
+      headers:
+        fields:
+        - [Content-Type, text/plain]
+        - [Content-Length, "5"]
+        # max-age=0 makes the cached response stale immediately.
+        - [Cache-Control, "max-age=0"]
+      content:
+        encoding: plain
+        data: stale
+
+    proxy-response:
+      status: 200
+      headers:
+        fields:
+        - [X-Cache, { value: "miss", as: equal }]
+      content:
+        encoding: plain
+        data: stale
+        verify: { as: equal }
+
+  #############################################################################
+  # Test 7: Valueless max-stale permits serving a stale response of any age
+  #############################################################################
+  - client-request:
+      # Allow the cache write from the preceding transaction to finish.
+      delay: 100ms
+      method: GET
+      url: /max-stale
+      version: '1.1'
+      headers:
+        fields:
+        - [Host, www.example.com]
+        - [Cache-Control, "max-stale"]
+        - [x-debug, "x-cache,x-cache-key,via"]
+        - [uuid, max-stale-serve]
+
+    proxy-request:
+      expect: absent
+
+    # The server response is a sentinel and must not be used.
+    server-response:
+      status: 502
+      reason: Bad Gateway
+
+    proxy-response:
+      status: 200
+      headers:
+        fields:
+        # ATS reports an acceptable-stale lookup as a fresh cache hit.
+        - [X-Cache, { value: "hit-fresh", as: equal }]
+      content:
+        encoding: plain
+        data: stale
+        verify: { as: equal }