In particular, there remain still open questions concerning scaling and universality in the late–stage growth kinetics. This has motivated several experimental investigations of ordering after a temperature quench, mostly on Cu$_3$Au, where direct information has been obtained from time–resolved X–ray diffraction and neutron scattering. On the other hand, only few theoretical or computer simulation studies on such materials have been reported so far .[@Lai; @Fron; @paper1] Frontera [*et al.*]{} [@Fron] have recently simulated the growth of $L1_2$–ordered domains both within an atom–atom exchange and the more realistic atom–vacancy exchange mechanisms, for quench temperatures below the expected spinodal temperature $T_{sp}$. A similar model with atom–vacancy exchange ($ABV$–model) was applied by Kessler [*et al.*]{} [@paper1] to surface–induced kinetic ordering processes near Cu$_3$Au(001).

In this paper we investigate the ordering kinetics in the bulk of such alloys at quench temperatures $T_f$ both below and above $T_{sp}$. In contrast to earlier Monte Carlo studies of nucleation in Ising–type models [@BindStauf; @StaufferA] we again employ the $ABV$–model with effective chemical interactions between nearest neighbors on the fcc–lattice. This allows us to compare our results directly with experiments on fcc–alloys, where vacancy–driven processes prevail. In particular, we analyze the nucleation regime, where we find a well 