Nonlinear optical crystals are important components of many laser systems. Prior to using such crystals for space applications, it must be clarified whether their optical properties will be negatively influenced by the omnipresent cosmic radiation. As part of an ESA project, extensive investigations are also carried out with different frequency doubling and frequency tripling crystals. For the investigations, the crystals were exposed in several steps to highly energetic proton and gamma radiation. In addition to the irradiation test, extensive long-term efficiency measurements for frequency doubling and tripling are also carried out. The objective is to determine the optimum crystals for application in space and to achieve an optical efficiency of more than 30 % for generating laser radiation at 355 nm.