The surface flatness of GaAs and InP mirror-polished wafers, which are typical III-V compound semiconductors substrates, is briefly reviewed with regard to the epitaxial-growth on them. The local thickness variation (LTV : 10 mm ^?? ) of 3-inch (100) wafers is less than 1 μm, which is sufficient to fabricate the integrated circuits for the present. On the mirror-polished wafers with native oxide layers, no steps, estimated from the macroscopic surface unevenness and/or the inclination of the wafer orientation, are observed. There is only an atomic-scale roughness with four monolayers in depth. On the other hand, monolayer steps and terraces are formed by the epitaxial growth under appropriate growth conditions. The studies on the control of the shape and spacing of the steps ranging from 100 μm to 8 nm are continued.