diff --git a/cloudpickle/cloudpickle.py b/cloudpickle/cloudpickle.py
index 4d532e5d..d8156155 100644
--- a/cloudpickle/cloudpickle.py
+++ b/cloudpickle/cloudpickle.py
@@ -96,6 +96,7 @@
 _DYNAMIC_CLASS_TRACKER_LOCK = threading.Lock()
 
 PYPY = platform.python_implementation() == "PyPy"
+GRAALPY = platform.python_implementation() == "GraalVM"
 
 builtin_code_type = None
 if PYPY:
@@ -410,10 +411,15 @@ def _builtin_type(name):
 
 def _walk_global_ops(code):
     """Yield referenced name for global-referencing instructions in code."""
-    for instr in dis.get_instructions(code):
-        op = instr.opcode
-        if op in GLOBAL_OPS:
-            yield instr.argval
+    if not GRAALPY:
+        for instr in dis.get_instructions(code):
+            op = instr.opcode
+            if op in GLOBAL_OPS:
+                yield instr.argval
+    else:
+        # GraalPy doesn't support disassembling bytecode, assume all names
+        # reference globals
+        yield from code.co_names
 
 
 def _extract_class_dict(cls):
diff --git a/tests/cloudpickle_test.py b/tests/cloudpickle_test.py
index 72aa132f..78ad74ea 100644
--- a/tests/cloudpickle_test.py
+++ b/tests/cloudpickle_test.py
@@ -190,6 +190,13 @@ def test_pickling_file_handles(self):
         out2 = pickle.loads(cloudpickle.dumps(out1, protocol=self.protocol))
         self.assertEqual(out1, out2)
 
+    @pytest.mark.skipif(
+        platform.python_implementation() == "GraalVM",
+        reason=(
+            "GraalPy doesn't support disassembling bytecode, so globals "
+            "cannot be distinguished from other names."
+        ),
+    )
     def test_func_globals(self):
         class Unpicklable:
             def __reduce__(self):
@@ -925,7 +932,7 @@ def test_builtin_classmethod(self):
     @pytest.mark.skipif(
         (
             sys.version_info >= (3, 10, 8)
-            and platform.python_implementation() == "CPython"
+            and platform.python_implementation() in ("CPython", "GraalVM")
         ),
         reason=(
             "CPython dropped support for pickling classmethod_descriptor,"