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This paper deals with consistency requirements of Peterson's algorithm for mutual exclusion of n processes in a distributed shared memory (DSM) system.It is shown here that a suitable combination of processor consistency and PRAM consistency, i.e. two models that are weaker than sequential consistency, is sufficient for the correctness of Peterson's algorithm for n processes. The algorithm resulting from the combination is proven to be correct in terms of safety and liveness including progress and lockout-freedom. Moreover, the combination is proven to be optimal for Peterson's algorithm in the sense that the relaxation of any write operation consistency semantics leads to incorrectness of the algorithm.