The aim of this paper is to study strong Karush-Kuhn-Tucker optimality conditions and duality for nonsmooth multiobjective semi-infinite programming. By using the Michel-Penot subdifferential and suitable generalized regularity conditions, we establish the strong necessary and sufficient optimality conditions for some kind of efficient solutions of nonsmooth multiobjective semi-infinite programming. We also propose Wolfe and Mond-Weir duality schemes for multiobjective semi-infinite programming and explore weak and strong duality relations under the generalized convexity.