This work, which is a continuation of a recent publication on the same topic (G.M. Kontogeorgis, P. Coutsikos, P. Tassios and Aa. Fredenslund, Fluid Phase Equilibria, 92 (1994) 35), presents a new theoretically-based G(E)-model (Chain-FV) for alkane systems. The model is based on a modified form of the generalized van der Waals partition function and attempts to account for all non-energetic effects of solutions of both short- and long-chain alkanes, including alkane polymers. Both the free-volume effects and the density-dependent rotational degrees of freedom are considered. The resulting G(E)-model which, despite its derivation from a partition function resembles the Flory-Huggins formula, is suitable for vapor-liquid and solid-liquid equilibrium calculations for nearly athermal polymer solutions as well as for alkane systems. We show that using plausible assumptions for the free-volume and the external-degree-of-freedom parameter, very good predictions are obtained for activity coefficients of asymmetric alkane systems at both concentration ends, for solid-liquid equilibrium calculations, as well as in extreme cases (polymer solutions, activity coefficients of heavy model alkane polymers in short-chain compounds recently available from molecular simulation studies). The predictions of the Chain-FV model are better than the Flory-Huggins and Elbro terms and equivalent to the recently proposed empirical R-UNIFAC and p-FV models. However, unlike the latter two models, the one proposed in this work offers a successful combination of simplicity and accuracy, with a solid theoretical basis.