A generalized nonisothermal particle-bed model for multicomponent adsorption-based separations is developed in this study. The multicomponent mass transport is described by the D'Arcy's law in the adsorbent bed and by the dusty-gas model in the adsorbent particles. No restrictions are imposed on the number of species in the multicomponent mixture. Appropriate boundary conditions are formulated for all the basic steps in an adsorptive separation scheme. The model is solved by a combination of the collocation and the subdomain methods of weighted residuals. A four-step pressure swing adsorption process for production of oxygen-enriched product from air using zeolite 5A as an adsorbent is employed as a model system for the application of the particle-bed model. The model is tested under various conditions of operations, and its predictions are discussed in the context of past analytical results and experimental observations. The results show that nonisothermal pressure swing adsorption processes approach their cyclic steady states very slowly because of the slow build up of the temperature profiles. II is also found that the external heat transport limitations at the outer surface of the adsorbent particles have no effect on the nonisothermal operation of the adsorbent beds, and it is thus concluded that a single energy equation for the macroscopic variation of the temperature in the bed would suffice in almost all practical applications. The particle-bed model is found to be superior to the lumped-parameter models for the case of strong intraparticle mass transport limitations.