We use a nearest-neighbor antiferromagnetic Ising model with spin-exchange dynamics to study by Monte Carlo simulations the dynamics of ordering in low-temperature quenched nonstoichiometric A xB 1 − x binary alloys. By implementing the conserved spin-exchange dynamics into the Monte Carlo method the system evolves so that the density is preserved while the order parameter is not. The simulations have been carried out on a two-dimensional square lattice and the stoichiometric value of the composition x is x 0 =0.50. By using different values of x ranging from 0.60≤x≤ x 0 =0.50, we study the influence of the off-stoichiometry on the dynamics of ordering. Regarding the behavior of the excess particles all along the ordering process, we obtain two different regimes. (i) At early to intermediate times the density of excess particles at the interfaces rapidly increases, reaching a saturated value. This density of saturation depends on both composition and temperature. As a consequence of this, since the disorder tends to be localized at the interfaces, the local order inside the growing domains is higher than the equilibrium value. (ii) Once saturation is reached, the system evolves so that the density of excess particles at the interfaces remains constant. During this second regime the excess particles are expelled back to the bulk as the total interface length decreases. We use two different measures for the growth: the total interface length and the structure factor. We obtain that during the second regime scaling holds and the domain-growth process can be characterized, independently on x, by a unique length which evolves according to l(t)∼ t n being n ∼ (0.50–0.40). Although the growth process tends to be slower as x increases, we find that the domain-wall motion follows the main assumptions underlying the Allen-Cahn theory. This is indicative that the coupling between diffusive excess particles and curvature-driven interface motion does not modify the essential time dependence but varies (slows down) the growth rate of the growth law, i.e., l(t)= k 1 / 2 xt , with k x decreasing with x. We suggest that the logarithmic growth experimentally observed in some nonstoichiometric binary materials has to do with the existence of specific interactions (not present in our case) between diffusive particles and domain walls. These interactions are of crucial importance in determining the essential time dependence of the growth law.