A comprehensive theoretical study of the problem of multicomponent adsorption-desorption in sorbent particles under pressure swing conditions is carried out in this study. A rigorous mathematical model is formulated for the process in which the dusty-gas model and the commonly used Fickian model are employed to describe the coupling of the mass fluxes and the partial pressures in the pore space, with or without viscous flow. The dusty-gas model is used as a standard against which the performance of the Fickian model is tested. Computations are carried out for binary and quaternary mixtures. It is found that the rigorous model (the one based on the dusty-gas model) predicts faster responses for the partial pressures of the components in the mixture, Faster responses are also observed when the viscous flow is accounted for in the transport model, with the effect-being considerably stronger in the case of the Fickian model. The obtained results are also used to investigate the performance of the Glueckauf linear driving force approximation for multicomponent systems. It is concluded that like the Fickian diffusion model on which it is based, this approximation cannot predict, even qualitatively, the dynamic responses of the partial pressures in a multicomponent system.