The aim of this work is to study optimality conditions for nonsmooth minimax programming problems involving locally Lipschitz functions by means of the idea of convexifactors that has been used in [J. Dutta, S. Chandra, Convexifactors , generalized convexity and vector optimization, Optimization, 53 (2004) 77-94]. Further, using the concept of optimality conditions, Mond-Weir and Wolfe type duality theory has been developed for such a minimax programming problem. The results in this paper extend the corresponding results obtained using the generalized Clarke subdifferential in the literature.