We consider coordinating accesses to shared data structures in multiprocessor real-time systems scheduled under preemptive global EDF. To our knowledge, prior work on global EDF has focused only on systems of independent tasks. We take an initial step here towards a generic resource-sharing framework by considering simple shared objects, such as queues, stacks, and linked lists. In many applications, the predominate use of synchronization constructs is for sharing such simple objects. We analyze two synchronization methods for such objects, one based on queue-based spin locks and a second based on lockfree algorithms.