A comprehensive algorithm has been developed for multiphase equilibrium computations in multicomponent systems. The algorithm includes stability analysis and calculation of equilibrium compositions by a combination of a multiphase direct substitution method and Gibbs energy minimization. The algorithm, has been specially designed to handle the numerical complexities that are characteristic of systems containing large (polymeric) and small molecules. Such complexities include a very strong composition dependence of equilibrium ratios (K-factors) as well as frequent occurrence of extremely low equilibrium concentrations and fugacity or activity coefficients.