A homotopy method for computing azeotropes in homogeneous multicomponent mixtures, developed by Fidkowski et al.,l has been generalized to include heterogeneous liquids. The method together with an are length continuation and a rigorous stability analysis and calculation of liquid-liquid equilibrium in multicomponent mixtures, developed by Wasylkiewicz et a1.,(2) gives an efficient and robust scheme for finding all homogeneous as well as heterogeneous azeotropes predicted by a thermodynamic model. A new, more general homotopy function has been proposed which reduces to the form proposed by Fidkowski et al.(1) for homogeneous liquid mixtures. Unlike the homogeneous case, turning points can often be found on solution branches leading to the heterogeneous azeotropes. A few examples for heterogeneous systems are shown and compared with results obtained using the homogeneous models.