Abstract. Monte Carlo simulations have been performed to investigate the relaxation of the L1 0 long-range order in dimensionally reduced systems. The effect of the number of (001)-type monatomic layers and of the pair interaction energies on these kinetics has been examined. The vacancy migration energies have been deduced from the Arrhenius plots of the relaxation times. A substantial increase in the migration energy for small film thickness is observed. The results agree with previous Monte Carlo simulations and with recent experimental results in L1 0 thin films and multilayers.