In this work, we consider multiobjective space mission design problems. We will start from the need, from a practical point of view, to consider in addition to the (Pareto) optimal solutions also nearly optimal ones. In fact, extending the set of solutions for a given mission to those nearly optimal significantly increases the number of options for the decision maker and gives a measure of the size of the launch windows corresponding to each optimal solution, i.e., a measure of its robustness. Whereas the possible loss of such approximate solutions compared to optimal- and possibly even 'better'-ones is dispensable. For this, we will examine several typical problems in space trajectory design-a biimpulsive transfer from the Earth to the asteroid Apophis and two low-thrust multigravity assist transfers-and demonstrate the possible benefit of the novel approach. Further, we will present a multiobjective evolutionary algorithm which is designed for this purpose.