A technique is proposed for the formation of epitaxial films of silicon carbide, gallium and aluminum nitrides on the surface of non-planar silicon parts. Using the technique, a GaN/AlN/SiC/Si heterostructure was grown on the surface of a silicon ring. The samples were studied by scanning electron microscopy, as well as raman and energy dispersive spectroscopy. It is shown that the preliminary deposition of a SiC layer on silicon by the atomic substitution method, in which (111) facets are inevitably being formed regardless of the local crystallographic orientation of the substrate surface, makes it possible to efficiently grow subsequent layers of III-nitrides of both wurtzite and sphalerite types on silicon parts.