Layer-by-layer growth of GaAs and GaAsXP1-X (x = 0.7-0.8) on nominally oriented (111) substrates has been performed by atomic layer epitaxy (ALE). The ideal growth rate of one monolayer per cycle was obtained on a (111)B substrate, but not on a (111)A substrate. Mirror-like smooth surface morphologies can be obtained on both (111)A and (111)B substrates in a wide range of growth conditions. The X-ray rocking curve of the GaAsxP1-x/GaAs multilayer sample grown on the (111)B substrate showing clear satellite patterns indicates abrupt interfaces that are superior to those of the (100) sample. It was also found that the disorder in growth such as the generation of hillocks can be reduced drastically by the ALE method.