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Periods of matrix power sequences in max-drast fuzzy algebra and methods of their computation are considered. Matrix power sequences occur in the theory of complex fuzzy systems with transition matrix in max-t algebra, where t is a given triangular fuzzy norm. Interpretation of a complex system in max-drast algebra reflects the situation when extreme demands are put on the reliability of the system. For triangular norm t= min, the matrix periods have been already described in literature. In this paper, a polynomial algorithm for computing the matrix period in max-drast algebra is presented, and the relation between matrix periods in max-min and max-drast cases is described.