This paper describes a procedure and first results for the prediction of critical points of nonideal systems with a UNIFAC-based equation of state. The PSRK group contribution model (Holderbaum and Gmehling, 1991) was incorporated in the computational method developed by Heidemann and Khalil (1980). The algorithm was extended on testing both local and global thermodynamic stability of calculated critical points. Predicted critical points of 15 binary systems were compared with experimental data. The test mixtures included aqueous solutions of inorganic gases, hydrocarbons, alcohols and carbon dioxide. Excellent agreement was obtained in cases when experimental VLE data covered a wide range of temperatures and pressures. For complex systems, a correlation method was suggested which may be useful to improve the predictive ability of group contribution methods for supercritical mixtures. Multicomponent critical points were predicted for 36 systems containing three to twelve components. The PSRK results were compared with the performance of the original SRK and SPHCT equations of state (Garcia-Sanchez et al., 1992).