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According to the results in Canto e Castro et al. , max-semistable distribution functions can be characterized by a parameter r > 1, by the extreme value index γ and by a real function w defined in [0,log r]. The estimation of the parameters r and γ based on ratios of differences of order statistics, or appropriate functions of these sequences, was treated in Dias and Canto e Castro . In this work we study the asymptotic distribution of these sequences of statistics.