The growth process of β-SiC on sapphire (0001) and (1102) planes and Si (111) plane by reactive evaporation of Si in C2H4 or C2H2 gas has been investigated by reflection high energy electron diffraction. Polycrystalline SiC films with stoichiometric composition were obtained when the ratio of the incidence frequency of reactive gas molecules to that of Si atoms, γ, was greater than 140 at the substrate temperature Ts= 770°C for C2H4 reactive gas, and when γ was greater than 25 at Ts= 700 °C for C2H2 gas. Using C2H2 gas, epitaxial films of SiC were grown on sapphire at 1000°C. However only polycrystalline films were grown on Si at Ts≤1200 °C. When the Si surface was covered with a SiC buffer layer, 500Å thick, deposited at 770 °C, SiC films were grown epitaxially on the Si substrates at 1000°C. From the analysis of IR transmittance of the films on Si, it was concluded that no hydrogen atoms are contained in the films deposited by the reactive evaporation.