This dissertation presents a global method to solve multi-objective hybrid optimal control problems. The method is applicable to general problems but the emphasis here is on space systems and missions. This holistic framework combines three main building blocks: a memetic multi-objective optimisation algorithm, a transcription method to solve general optimal control problems, and the treatment of mixed integer problems. The framework is able to automatically produce a well spread set of Pareto optimal solutions, each of which can consist of an optimal open loop guidance law and system design parameters, which can include the set and order of targets or operations that compose the structure of a mission. The framework was employed to perform the multi-objective trajectory and system design of reusable launch vehicles, including the sizing the engines, structural masses, fuel tanks and wings, and to design a multiple target debris removal space mission in which the trajectory of the spacecraft and the sequence in which the targets are visited had to be simultaneously optimised.