  We consider a multi component mixture of inert gas in the kinetic regime by
assuming that the total number of particles of each species remains constant.
In this article we shall illustrate our model for the case of two species. To
account for thermal effects, we extend a BGK model based on the presence of a
collision term for each possible interaction \cite{Pirner} by including ES-BGK
effects. We prove consistency of the extended model like conservation
properties, positivity of all temperatures, H-theorem and convergence to a
global equilibrium in the shape of a global Maxwell distribution.
