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We are interested in the process of partial maxima [\\tilde M_n(u,t) =\\max \\{X_{in}(t), 1 \\leq i\\leq [nu]},\\quad u\\geq 0,\\ t\\in T.] where the brackets $[\\,\\cdot\\,]$ denote the integer part. Under a regular variation condition on the sequence of processes $X_n$, we prove that the partial maxima process $\\tilde M_n$ weakly converges to a superextremal process $\\tilde M$ as $n\\to\\infty$. 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