  Starting from a microscopic approach, we develop a covariant formalism to
describe a set of interacting gases. For that purpose, we model the collision
term entering the Boltzmann equation for a class of interactions and then
integrate this equation to obtain an effective macroscopic description. This
formalism will be useful to study the cosmic microwave background
non-perturbatively in inhomogeneous cosmologies. It should also be useful for
the study of the dynamics of the early universe and can be applied, if one
considers fluids of galaxies, to the study of structure formation.
