For the robust multiobjective optimization problem involving nonsmooth/nonconvex real-valued functions，the sufficient optimality conditions for robust (weakly) Pareto solutions are established. In addition，weak and strong duality relations of the dual multiobjective problem are explored. Using the limiting subdifferential of the compound function，the optimality condition of the optimization problem can still be obtained under the condition of (strictly) generalized pseudoconvex，and the strong and werk duality can be established by the dual problem. Finally，under the condition of (strictly) generalized pseudoconvex，three theorems are obtained and proved.