We have investigated via Monte Carlo simulations the microstructure of the CuAu-I ordered phase in III-V semiconductor alloys of (A 1Ϫx B x )C grown on ͑001͒ substrates. The Fourier power spectra of atomic configurations in the computer-generated structures could reproduce the features of the electron-diffraction patterns reported previously. Among the three possible variants of the CuAu-I structure, a simulated ͑001͒ epilayer contains two variants which have their tetragonal c-axis parallel to the ͑001͒ plane. We have found that the CuAu-I ordering occurs even in an off-stoichiometric alloy with xϭ0.25, but a low-deposition rate at a low growth temperature forms a short-range-order state of a