Excess Gibbs energy models based on the local composition concept are applied to the description of the solid-liquid equilibria of paraffins. The energetic parameters used by these models are estimated 'a priori' by relating the interaction energies between pairs of molecules with their enthalpies of sublimation providing a pure predictive model for the description of solid-liquid equilibria of systems with n-alkanes. This procedure for parameter estimation is successfully applied to the NRTL and UNIQUAC models. They provide a very good description of the composition of the phases in equilibrium, along with the fraction of crystallised solution. These models make possible to overcome the inability of the Wilson equation to model a phase split in the solid phase. It is shown that the limit for complete miscibility in the solid phase is attained when the difference in chain length between two linear alkanes is of about three carbons. This limit is in a fair agreement with the Limits presented by other authors.