To avoid the complexity of the Boltzmann collision operator, the BGK Model Equation is widely used, but it is well known that one of its shortcoming is that it gives a Prandtl number of one in the fluid limit. The ES-BGK was introduced to obtain the correct Prandtl number, but the entropy property for this model was an open problem. In this talk we prove that this model actually verify an H theorem. Moreover we show in a simple case that computations with this model are of the same order of complexity and cost as with the BGK model, so that it appears as a valid alternative of the BGK model. ©2001 American Institute of Physics.