Single crystals of chromium-doped LiCAF and LiSAF can be grown from nearly stoichiometric melts of the components LiF, AlF3, CrF3 and CaF2 or SrF2, respectively, by the Czochralski method. The optical quality of LiSAF crystals is usually better, as LiCAF contains more scattering particles. This different behavior can be attributed to different thermodynamic properties of both substances: The higher melting point of LiCAF leads to higher evaporation losses of volatile LiF and AlF3. Moreover, LiCAF melts incongruently. The main problem during the growth and application of LiSAF crystals is the highly anisotropic thermal expansion that may lead to thermal cracking. The extreme hygroscopicity of the doping agent CrF3 has to be considered for the growth of both substances.