A method to compute binary homogeneous azeotropes in multi-component mixtures at elevated pressures through the equation of state approach is developed. The method is capable of predicting the homogeneous azeotropes and is in close agreement with experimental data. At higher pressures, vapor and liquid phase non-idealities are incorporated using vapor and liquid phase fugacity coefficients from Peng-Robinson-Stryjek-Vera equation of state with Wong-Sandler mixing rules. The method is also capable of predicting the exact value of bifurcation pressure where homogeneous azeotropes may appear or disappear. The method can predict the azeotropes at elevated pressures and is independent of equation of state and mixing rules. The method is also capable of predicting the double azeotropy in binary mixtures. The method is tested with Ethanol-Water, Isopropanol-Water, Carbon dioxide-Ethane-Ethylene and Ammonia-R-125 systems. The highly non-linear system of equations is solved by homotopy continuation approach. (C) 2003 Published by Elsevier Ltd.