Molecular beam epitaxy (MBE) growth of CdF2 and CaF2 layers and nanoscale heterostructures on Si(1 1 1) and Si(0 0 1) substrates has been investigated. The surface morphology of CaF2 and CdF2 layers on Si(1 1 1), studied by atomic force microscopy (AFM) was found to depend strongly on the growth temperature. The high temperature 2D growth mode would produce atomically Rat surface. In contrast to that, well-pronounced pyramids indicating the 3D growth mode were observed on the layers grown at low temperature, Short-period CdF2-CaF2 superlattices (SLs) were also studied. Analysis of reflection high energy electron diffraction (RHEED) intensity oscillations showed asymmetry of the "CaF2 on CdF2" and "CdF2 on CaF2" interfaces resulting in SL surface smoothening. The possible mechanisms relevant to this phenomenon have been discussed. Atomic force microscopy (AFM). and RHEED have been used to study formation of CaF2 epitaxial nanostructures on Si(0 0 1). Different types of nanostructures have been grown including ultra-thin 2D wetting layer, quasi ID wires at high growth temperature and well-organized dots at lower temperatures. An important role of the wetting layer in the transformation of the surface morphology at the initial stages of CaF2 growth on Si(0 0 1) at high temperatures has been demonstrated.