  We consider a multi component gas mixture with translational and internal
energy degrees of freedom assuming that the number of particles of each species
remains constant. We will illustrate the derived model in the case of two
species, but the model can be easily generalized to multiple species. The two
species are allowed to have different degrees of freedom in internal energy and
are modelled by a system of kinetic ES-BGK equations featuring two interaction
terms to account for momentum and energy transfer between the species. We prove
consistency of our model: conservation properties, positivity of the
temperature, H-theorem and convergence to a global equilibrium in the form of a
global Maxwell distribution. Thus, we are able to derive the usual macroscopic
conservation laws. For numerical purposes we apply the Chu reduction to the
developed model for polyatomic gases and give an application for a gas
consisting of a mono atomic and a diatomic species.
