A modified statistical associating fluid theory (SAFT) equation of state has been applied to predict the phase equilibria behavior of binary and ternary mixtures. In order to study multicomponent systems, the equation is first applied to pure fluids. The SAFT equation is written in the same spirit as that presented by Huang and Radosz [Ind. Eng. Chem. Res. 1990, 29, 2284-2294], but with two important differences : the reference term is a Lennard-Jones fluid, accounting explicitly for dispersive and repulsive forces, and the equation is extended to heteronuclear chains. The molecular parameters of pure substances are obtained by fitting to the saturated liquid density and by equating the chemical potentials in both phases. Three molecular parameters are needed to obtain the thermodynamic properties of pure substances, namely, the segment size, dispersive energy, and chain length. Two additional parameters are needed to describe the associating molecules, the association energy, and volume. They are obtained by fitting to experimental saturated liquid density and by equating the chemical potentials in both phases over a wide range of temperatures. The molecular parameters are found to scale with the molecular weight for the alkanes. The binary parameters of the mixtures, xi(12) and eta(12) in the generalized Lorentz-Berthelot combining rules, are fitted to experimental data for the molar fractions on the Liquid and vapor sides at a given temperature, in such a way that they do not depend on the composition and/or temperature. These binary parameters are used to predict the behavior of the mixture at different thermodynamic conditions. Ternary mixtures are predicted from the previous parameters without any further adjustment. The agreement between prediction and experimental results is excellent in all cases.