The steady-state operation of a simulated moving bed (8MB) process can be modeled by that of an equivalence true countercurrent (TCC) adsorption unit. An equilibrium theory based on the TCC unit is very useful for the selection of a proper condition to operate an 8MB process. The exact analysis of such an equilibrium model, however, has been limited to systems following a constant selectivity stoichiometric isotherm, which is not frequently observed. In this article, the equilibrium theory was extended to a multi-component system that follows a constant selectivity nonstoichiometric isotherm. An exact solution is presented for the complete separation regions on the parameter space. The analysis is further applied to cases where only partial separation can be achieved.