In GaAs and AlAs atomic-layer epitaxy (ALE), it was experimentally found that the AlAs layer is deposited in two monolayers (2 ML) per ALE cycle, while the GaAs layer is deposited in 1 ML. In order to elucidate this growth mechanism, we compared the stability of Ga and Al atoms on the GaAs(100) surface by the first-principles total energy calculation based on density functional theory. Comparing adsorption energies, we found that Ga and Al stably adsorbed on the As-Terminated GaAs surface in 1 ML. It was also revealed that Al can adsorb on an As-Terminated GaAs(100) surface in 2 ML because excess Al atoms can be adsorbed by forming a metallic Al(110) plane-like structure. These results well explain the experimental results for ALE-GaAs and ALE-AlAs.