Atomic layer epitaxy of cubic SiC was investigated to examine gas reactions on the surface at high temperature using Auger electron spectroscopy and low energy electron diffraction. Self-limiting growth at one and one-third atomic monolayers at 1050-degrees-C was observed for exposure of a carbon-terminated surface to Si2H6, and self-limiting growth at just one atomic monolayer was observed for exposure of a silicon-saturated surface to C2H2. It was also found that the extra partial silicon layer of the silicon-saturated surface desorbs during C2H2 exposure. By alternating exposure to Si2H6 and C2H2, accurate layer-by-layer growth is achieved. In this system, the spontaneous atomic layer desorption of silicon which occurs during C2H2 exposure is consistent with the nature of exact atomic layer epitaxy.