An algorithm for calculating the boiling point pressure at a chosen temperature and composition was used for computing liquid-liquid equilibrium. A lot of attention is paid to the determination of the first approximation which is specified in terms of the conditions of thermodynamic stability. The conditions of thermodynamic stability make as well possible to localize the lower and upper critical end points (LCEP and UCEP. The Redlich-Kwong-Soave equation of state was applied in calculations, and it was found out that this equation with zero interaction parameters predicts well the lower and upper critical end temperatures in the systems methane-n-hexane, ethane-n-eicosane and ethane-n-docosane.