In this work, a nonsmooth multiobjective optimization problem involving gen-eralized invexity with cone constraints (for short, (MOP)) is considered. The Kuhn-Tucker necessary and su?cient conditions for (MOP) are established by using a generalized alterna-tive theorem of Craven and Yang. The relationship between saddle points and weakly effcient solutions of (MOP) is developed. Furthermore, the Wolfe type and Mond-Weir type weak, strong and converse duality results for (MOP) are presented. These results extend and improve corresponding results of others.