A stochastic model is proposed for the study of the effect of the interactions on transport through a system placed between two parallel external baths. The exchange of matter of a system at local equilibrium with a single external bath is conveniently treated with the help of a stochastic theory described previously. That theory is extended here to the case of a system placed between two parallel external baths. The extension is realized as follows. The system is viewed as an array, perpendicular to the external gradient, of hypothetical layers at local equilibrium. Each layer exhibits a ’’two-faced exchange,’’ exchanging matter with two baths (viz., layers on its two sides) and provides, in turn, a bath to these two layers. The theory is applied to a study of the steady state properties of far from equilibrium systems composed of two and of three molecular species. It is shown that, in the case of a binary system, our two-faced exchange model leads to an equilibrium in each layer, whatever the value of the external gradient. However, that convenient feature evaporates on passing to systems with more than two molecular species. The effect of the interactions on the stationary flows and concentration profiles is extensively studied. The relevance of our results to the diffusion of hydrogen through palladium is also discussed.