SiC and SiC-AlN solid solution have been grown by container-free liquid phase epitaxy (CFLPE) from the silicon melt suspended in a high frequency electromagnetic field. Substrate temperature was 1450-1700-degrees-C. The substrates were 6H-SiC crystals with a {0001} basal-plane orientation. Aluminum (acceptor) and nitrogen (donor) have been used as impurities. Growth rate of 6H-SiC layers was controlled in the range of 0.02 to 2 mum/min. Layers were single crystal. The concentration N(d) - N(a) was varied in the range of 8 x 10(15) to 1 X 10(19) cm-3. For p-type layers, aluminum concentration was controlled from 1 x 10(18) to 2 x 10(20) cm-3. Heteroepitaxial 3C-SiC layers have been grown on 6H-SiC substrates from the liquid state. Minimum half-width of the X-ray rocking curve of 3C-SiC layer was 11.5 arc sec. A red-light-emitting diode has been fabricated based on a 3C-SiC/6H-SiC p-n heterojunction. Single crystal SiC-AlN solid solution layers with AlN concentration up to 10 mol% have been grown by CFLPE.