The local composition models of NRTL and UNIQUAC have been used in predicting of azeotropic data for binary and ternary liquid mixtures of various types. Activity coefficients have been calculated using the temperature dependent parameters of the models. In order to avoid the convergence problem of Newton's method due to initializing the unknowns,the step controlled Newton's method has been used. The results show that the performance of the UNIQUAC model is slightly better than that of the NRTL model. However the performances of the models change from one mixture to another.