Shock layers (constant patterns), which propagate with constant velocity without changing their shape, can develop in adsorption units under suitable operating conditions. They have been observed both in experiments as well as in numerical computations. By extending the approach and the results of two solute chromatography (Rhee and Amundson, 1974, Chem. Engng Sci. 29, 2049-2060), in this paper we develop the shock layer theory for multicomponent adsorption processes in fixed-bed and in countercurrent columns, where the adsorption equilibria are described by Langmuir-type adsorption isotherms. Two different models to describe the adsorption-diffusion process in the solid particles have been considered : the solid diffusion model and the pore diffusion model. Explicit expressions for the concentration profiles across the shock layer as well as for its propagation velocity are reported for the general class of multicomponent systems and column configurations mentioned above. The reliability of the theoretical results has been assessed by comparison with both numerical results and experimental data.