The growth of PbTe films on GaAs by molecular beam epitaxy was studied by reflection high energy diffraction. The strains in the films were investigated by X-ray diffraction. Despite a lattice mismatch of 14.2%, oriented films can be grown up to a thickness of 4000 Å. For thicker films the thermal strain causes cracks if the samples are cooled from growth to liquid-nitrogen temperature. © 1988.