Monte Carlo simulations of the isothermal long-range order (LRO) relaxation in A3B system with Ll2 superstructure have been performed within a model based on a vacancy jump mechanism between nearest neighbour lattice sites. The studies aimed at the explanation of the origin of two simultaneous LRO relaxation processes experimentally observed in Ni3Al. An effect of pair interaction energies and saddle-point energies (assigned to jumping atoms) was studied. The preference of vacancies for the A-sublattice (face centres), commonly postulated for Ni3Al, occurred only for a narrow range of pair-interaction energies within the domain corresponding to Ll2 ordering. It was found that the appearance of the fast relaxation process is definitely correlated with the efficiency of B-atom jumps, as well as with the values of the saddle-point energies. The results lead to a microscopic model of the “order-order” relaxation in Ll2 superstructure and yield new indications for the choice of pair-interaction energy parameters applied in Monte Carlo simulations of atomic migration in Ll2 intermetallic compounds.