The phase equilibria of the n-alkanes and the 1-alkanols have been calculated with the Lennard-Jones-SAFT (statistical association fluid theory) equation of state of Muller and Gubbins. This equation includes contributions from a dipole-dipole term, a modified association term, a chain term, and a Lennard-Jones term to account for monomer dispersion and overlap interactions. The influence of electrostatic forces due to the dipole moment has been investigated, and a simple treatment of the polarizability has been tested. It is shown by comparison with some sample calculations based on the renormalized perturbation theory that this approach is reasonable. The calculated phase equilibria are in good agreement with experimental data. The deviation between calculated and experimental data is significantly lower than for the original SAFT equation of state and a recently published chemical theory.