Solid-liquid phase diagrams are calculated for systems containing pure Lennard-Jones dumbbell molecules and their mixtures. We begin by calculating the equations of state for systems containing C2H6, CO2 and F-2, all of which are modeled by a two-center Lennard-Jones potential for linear diatomic molecules. We then use the Frenkel-Ladd thermodynamic integration method to calculate the free energies. The equations of state and the free energies are used to obtain solid-liquid coexistence points which are needed to start the Gibbs-Duhem integration. The solid-liquid phase equilibria for pure C2H6, CO2 and F-2 and binary mixtures of Lennard-Jones dumbbells are predicted using the Gibbs-Duhem integration method. We investigate the effects of molecular size and intermolecular attractions on the solid-liquid phase diagrams of binary Lennard-Jones mixtures. (c) 2007 Published by Elsevier B.V.