In this paper, we derive first- and second-order necessary optimality conditions of Karush-Kuhn-Tucker type for H-locally weak solutions in the sense of Pareto of multiobjective optimal control problems with free right end point and free end-time and with mixed pointwise constraints. To deal with the problem, we first establish first- and second-order optimality conditions for a reduced problem with fixed end-time. We then obtain optimality conditions for the original problem.