A direct calculation method for critical endpoints has been developed on the basis of the algorithm for critical points from Heidemann and Khalil. Hereby, the Gibbs tangent plane criterion in the formulation of Michelsen was applied for the determination of the occurrence of an additional phase. Some results obtained with the Peng-Robinson equation of state for the ternary systems carbon dioxide + 1-hexanol + tridecane and carbon dioxide +- 1-pentanol + tridecane are compared to experimental critical endpoint data. The difficulties encountered with variation of the binary interaction parameters are discussed. Qualitative agreement between the calculated and the experimental data was obtained.