Two different numerical techniques, applying either the SRK or the PC-SAFT equations of state, were used to predict the multiphase behavior exhibited by the ternary systems nitrogen + methane + ethane, nitrogen + methane + propane, and nitrogen + methane + n-butane. The predictions with both equations of state were compared against experimental data in terms of nitrogen mole fractions of the two liquid phases and it was demonstrated that the agreement is good. Furthermore, a procedure similar to that reported by Gregorowicz and de Loos, in conjunction with the SRK equation of state, was introduced. It was applied to predict the K (L-1-L-2=V) and LCST (L-1=L-2-V) critical end points at constant temperature for the systems studied, and demonstrated a reliable and robust performance with good convergence characteristics.