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The statistical-thermodynamic theory of ordering and electronic theory of ordering in the pseudo-potential approximation was used to study the influence of ternary addition of some transition metals on the atomic ordering behavior of Co0.5(Ti1-xMx)0.5 alloys with M = Fe, Pt, Re, V, Cr, Mn, Ni, Cu, Zn, Zr, Ag, Hf or Au up to a concentration of 1 at.%. The partial ordering energies, order-disorder phase transformation temperatures and partial short range order parameters have been calculated for these alloys. The analysis shows that the impurity elements in Co0.5(Ti1-xMx)0.5 alloys can be divided into two main groups on the basis of lattice site occupancy i.e. M = V, Cr, Mn, Cu, Zn, Zr, Ag, Hf and Au mainly substitute for Co sublattice sites whereas M = Fe, Ni, Pt or Re mainly substitute for Ti sublattice sites. Further, the order-disorder transformation temperatures were found to either increase or remain nearly unchanged by the addition of ternary impurities in the CoTi alloy depending on the absolute value of the partial ordering energies. Alloys of Ti with V, Cr, Mn, Cu, Zn, Zr, Ag, Hf or Au in place of Co and alloys of Co with Fe, Ni, Pt or Re in place of Ti can be predicted for future. The results of the present analysis are in good agreement with the available experimental data on these alloys. [ABSTRACT FROM AUTHOR]