Remarkable high-temperature mechanical properties of nickel-based superalloys are correlated with the arrangement of ternary alloying elements in L1(2)-type-ordered. gamma '-Ni3Al intermetallics. In the current study, therefore, hightemperature site occupancy preference and energeticstructural characteristics of atomic short-range ordering (SRO) of ternary alloying X elements (X = Mo, W, Ta, Hf, Re, Ru, Pt or Co) in gamma '-Ni3Al 21.875 X 3.125 alloy systems have been studied by combining the statistico-thermodynamical theory of ordering and electronic theory of alloys in the pseudopotential approximation. Temperature dependence of site occupancy tendencies of alloying X element atoms has been predicted by calculating partial ordering energies and SRO parameters of Ni-Al, Ni-X and Al-X atomic pairs. It is shown that, all ternary alloying element atoms (except Pt) tend to occupy Al, whereas Pt atoms prefer to substitute for Ni sub-lattice sites of Ni 3 Al intermetallics. However, in contrast to other X elements, sublattice site occupancy characteristics of Re atoms appear to be both temperature-and composition-dependent. Theoretical calculations reveal that site occupancy preference of Re atoms switches from Al to both Ni and Al sites at critical temperatures, T c, for Re > 2.35 at%. Distribution of Re atoms at both Ni and Al sub-lattice sites above T c may lead to localised supersaturation of the parent gamma '-Ni3Al phase and makes possible the formation of topologically close-packed (TCP) phases. The results of the current theoretical and simulation study are consistent with other theoretical and experimental investigations published in the literature.