We present molecular dynamics (MD) simulation results on the role of vacancy diffusion in the surface order of the Cu3Au(001) and Ni3Al(001) faces. We found that in both systems vacancy diffusion proceeds preferably by hopping along the [110] direction. In the Cu3Au(001) case, successive vacancy diffusion events induce irreversible loss of the surface order, while in the Ni3Al(001) system each vacancy hop leads to unstable atomic arrangements having a clear preference of recovering the initial surface order. These findings can be used for the understanding of the order-disorder transition occurring in the Cu3Au(001) surface and the order-order kinetics characterizing the Ni3Al(001) face. In addition, we found that in the former case the vacancy diffusion rate saturates quickly (in <1 ns) and that it is correlated with the surface order parameter which reveals important disorder already at 500 K. In the later system, Al and Ni vacancies have constant hopping frequencies that exhibit Arrhenius behavior, while surface disorder is also predicted at high temperatures. (C) 2002 Elsevier Science B.V. All rights reserved.