Surface structure transitions during alpha -SiC{0001} homoepitaxy in a high vacuum were studied based on an in-situ. RHEED analysis. The reversible surface structure transitions ((1x1)reversible arrow (3x3) and (1x1)reversible arrow (2x2)) around 1150 degreesC were observed only with Si adsorption on (0001)Si- and (0001)C-faces. alpha -SiC: growth was carried out by gas source molecular beam epitaxy, and homoepitaxial layers could be grown on the Si- and C-faces above 1150 degreesC with an alternate supply of source gases. An activation energy of about 32.5 kcal/mol was obtained in the SIC growth.