A theoretical analysis of multicomponent adsorption in continuous countercurrent exchangers is presented. The system is considered to be one-dimensional, isothermal, locally at equilibrium, and to have negligible diffusion effects. With constant initial and entry data the mathematical problem is essentially the same as for a fixed bed except for the boundary condition that suggests a free boundary analogue since it is given by the conservation law itself. Therefore, the boundary discontinuity is naturally encountered. With the Langmuir adsorption isotherm explicit forms for the Riemann invariants and characteristic parameters are available and thus the theories of simple waves and of shock waves as well as of interactions are readily established and applied to determine solutions. Dependence of the system behaviour upon the flow rate ratio is discussed and the steady-state argument proves that the number of steady states attainable in the contacting region is equal to the number of solute species present plus one. Application is illustrated.