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In this article, we prove that the Cauchy problem for a N-dimensional system of nonlinear wave equations utt-a△utt=△f(u,v), x∈R N,t>0, vtt-a△vtt=△g(u,v), x∈RN ,t>0 admits a unique global generalized solution in C3 ([0,∞); W m,p (R N )∩L∞(RN)∩L2(R N