A multiobjective problem with a feasible set defined by inequality， equality and set constraints is considered， where the objective and constraint functions are locally Lipschitz. A generalized Stampacchia quasi vector variational inequality is formulated as a tool to characterize approximate quasi or weak quasiefficient points. By using two new classes of generalized convexity functions， under suitable constraint qualifications， the relations between KuhnTucker vector critical points， solutions to the multiobjective problem and solutions to the generalized Stampacchia vector variational inequality in both weak and strong forms are proved.