The effects of substitutional ternary additions of Me = Zn, Ti, Si, Cr, Mn, Mo, W, Nb, Ta, V, Hf, or Zr on the energetical and structural characteristics of atomic short-range ordering (SRO) of Ni-3(Al(1-x)Me(x)) intermetallics with L1(2) type ordered structure have been analysed by combining the statistical theory of ordering with the electronic theory of alloys in pseudopotential approximation. The partial ordering energies and pairwise SRO parameters were calculated by taking into account the influence of the first three coordination spheres. The results of calculation show that the atoms of Zn, Ti, Si, Mo or V elements substitute mainly for Al sublattice sites, whereas W, Nb, Ta, Hf, or Zr clement atoms substitute preferentially for the Ni sublattice sites and Cr or Mn element atoms tend to substitute for both Ni and Al sublattice sites. These theoretical results are in a good qualitative agreement with experimental observations for most of the third component Me elements. Copyright (C) 1997 Acta Metallurgica Inc.