A comparison is made of the capabilities of various equation of state (EOS) + excess free energy (G(ex)) models in representing the activity-coefficient models they incorporate. Such EOS models need to reproduce the excess Gibbs free energy behavior of the activity-coefficient models as closely as possible in order to represent low-pressure vapor-liquid equilibrium behavior of complex mixtures accurately, and also to make accurate the vapor-liquid predictions at higher temperatures and pressures using only low-pressure information. It is demonstrated that the EOS models that use the excess Helmholtz free energy instead of the excess Gibbs free energy, and that combine the EOS with activity-coefficient models at the infinite pressure limit, are successful for calculations of the type just described.