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This paper proposes to use a logical hypercube structure for detecting message stability in distributed systems. In particular, a stability detection protocol that uses such a superimposed logical structure is presented, and its scalability is compared with other known stability detection protocols. The main benefits of the logical hypercube approach are scalability, fault-tolerance, and refraining from overloading a single node or link in the system. These benefits become evident both by an analytical comparison and by simulations. Another important feature of the logical hypercube approach is that the performance of the protocol is in general not sensitive to the topology of the underlying physical network.