Optical phase conjugation (OPC) provides a means of dynamical correction of thermally induced aberrations in high-power laser systems. This method is particularly interesting for space applications because it is passive, mechanically simple, and allows for improved beam quality with only a small loss in power. To exploit it one has to assess the effect of the space environment, and in particular of space radiation, on the properties of the materials that are suitable for phase-conjugating mirrors (PCMs). We have investigated both materials providing OPC via stimulated Brillouin scattering and actual PCMs with regard to their radiation hardness. Proton- and gamma-irradiated PCMs in the form of 30-cm long silica rods and 5\text{- cm} long {\text{TeO}}_{\text{2}} crystals were tested in a single frequency flash-lamp pumped Nd:YAG system delivering up to 220\text{\hspace{0.17em} mJ} pulses with a \text{20 \hspace{0.17em} ns} duration at a \text{50 \hspace{0.17em} Hz} repetition rate. The difference in the reflectivity between irradiated and nonirradiated components was found to be within the measurement errors. Gamma irradiation of {\text{TeO}}_{\text{2}} resulted in a decrease of the laser-induced damage threshold, while for silica possible changes were below the detection limit. Our results show that synthetic fused silica, and Lithosil in particular, can be used for generating the OPC in laser systems operating in a space radiation environment.