Narayanan, K.V. and Ananth, M.S., 1993. Excess Gibbs free energy of mixing. Fluid Phase Equilibria, 91: 77-86. The statistical mechanical approach to developing excess Gibbs free energy models for liquids using lattice theories in the Canonical ensemble is reexamined numerically in the light of the fundamental observations of Sandler et al. (S.I. Sandler et al., 1989. Fluid Phase Equilibria, 45: 251-265). Calculations are carried out for mixtures of hard sphere fluids and model mixtures of Lennard-Jones (LJ) molecules to find the effect of varying the relative size of the hard sphere molecules and the unlike interaction parameters for LJ mixtures on the difference between the excess Gibbs free energy at constant pressure and the excess Helmholtz free energy under different mixing constraints. It is shown that for engineering purposes lattice theories can only provide mathematical expressions that fit mixture data accurately provided these expressions contain one or two adjustable parameters. Further, for fitting excess Gibbs free energy data it is shown that expressions for the excess Helmholtz free energy under any of the constraints ("Scatchard mixing", mixing under constant number density or constant reduced density) are equally useful. © 1993.