Nonequilibrium molecular dynamics calculations have been carried out o Lennard-Jones binary mixtures with the aim to investigate the dependence of the Soret coefficient on the temperature and on the composition for systems presenting phase transitions. By an appropriate choice of the cross interaction parameter, ε12 (0< ε12 <min { ε11, ε22 }), these systems show a mixing/demixing (consolute) phase transition. The other parameters are those of a binary mixture of Argon and Krypton. This system has been considered over a wide range of temperatures (up to ≃1000 K), of compositions (0.1≤ x1 ≤0.9), and of cross interaction parameter (0< ε12 <min { ε11, ε22 }). The study allows the formulation of a very simple expression for the Soret coefficient, S T, as a function of temperature and composition. Indeed the computed values of ST in the one phase region outside the critical region are closely fitted by the function [T- Tc (x1)] -1 where Tc (x1) is the demixing temperature of the mixture under study. This result indicates for this type of systems a dependence of S T, as a function of the temperature, on a unique characteristic property of the fluid mixture, the demixing temperature Tc, which, in turn, is a function of the binary mixture composition x1. © 2010 American Institute of Physics.