The evolution of atomic ordering processes in Ni3Al has been modelled by a Monte Carlo ( MC) simulation method combined with the electronic theory of alloys in pseudopotential approximation. The magnitudes of atomic ordering energies of atomic pairs in the Ni3Al system have been calculated by means of electronic theory in pseudopotential approximation up to the 4th coordination spheres and subsequently used as input data for MC simulation for more detailed analysis for the first time. The Bragg - Williams long- range order (LRO) and Cowley - Warren short-range order (SRO) parameters have been calculated from the equilibrium configurations attained at the end of the MC simulation for each predefined temperature and Al concentration levels which reveal the evolution of the system from the L1(2) -> disordered state as the temperature increases. The values of the LRO and SRO parameters at temperatures below 800 degrees C justify the existence of L1(2)-type ordered Ni3Al alloys for all concentration levels whereas at temperatures above 850 degrees C, the values of the LRO parameter implies the presence of a disordered solid solution of Ni3Al alloys. However, a higher degree of the SRO order parameter above the predicted order - disorder transition temperature is preserved up to the melting point of Ni3Al intermetallics. The composition dependence of the LRO and SRO parameters agrees well with the experimental results.