The structure of solutions of the nonrandom two-liquid (NRTL) model for prediction of liquid-liquid equilibria is investigated in ternary and quaternary systems. We graphically analyze the isoactivity equations of a ternary system and examine the structure of their solutions. Three types of solutions are revealed. In addition, we find that the convexity check of the Gibbs free energy does not always exclude erroneous predictions for either ternary or quaternary systems. Finally, we propose a procedure to identify the correct predictions as well as to investigate the structure of solutions of isoactivity equations, which works effectively for tested ternary and quaternary systems and theoretically is applicable to systems with multiple components. Both the graphical analysis method and the proposed procedure are transferable to analyzing liquid-liquid equilibria based on other thermodynamic models.