For studies of crystal quality and strain relaxation in heterostructures with epitaxial CdF2 and CaF2 layers on Si(lll), differential double crystal x-ray diffractometry and impurity photoluminescence techniques were used. The crystalline quality of molecular beam epitaxy grown CdF2 layers can be high and comparable with that of III-V compound pseudomorphic heterostructures. The best results were obtained for CdF2 layers grown on CaF2 buffer layers which were coherent with the Si substrate.