A rigorous model for multi-component adsorbers is developed. This considers non-isothermal effects, pressure variations, axial dispersion of components inside the gas (macro-void) phase as well as the diffusion of components inside the particles (micro-void). The partial differential equations (PDEs) for the gas phase are converted into ordinary differential equations (ODEs) or algebraic equations, using the finite difference technique in the axial direction. The method of orthogonal collocation (OC) is used to convert the PDEs for the diffusion inside the particles into ODEs. The complete set of differential-algebraic equations (DAEs) is solved using the Petzold-Gear technique. Data on two systems [O-2-N-2 on Zeolite 5A (Jee et al., 2002 [Jee, J. G., Park, M. K., Yoo, H. K., Lee, K.,& Lee, C. H. (2002). Adsorption and desorption characteristics of air on zeolite 5A, 10X, and 13X fixed beds, Separation Science and Technology, 37, 3465-3490]), and CO2-C2H6-N-2 on Linde 5A molecular sieves (Basmadjian and Wright, 1981 [Basmadjian, D., & Wright, D.W. (1981). Non-isothermal sorption of ethane-carbon dioxide mixtures in beds of 5A molecular sieves. Chemical Engineering Science, 36, 937-940])] are taken from the literature for validation of this model. The optimal values of the model parameters are obtained using one set of experimental data for each of these systems. Genetic algorithm is used for this purpose. Excellent agreement is observed between the predictions of the tuned model and the experimental data used. In addition, it was observed that the predictions of the tuned model agree quite well with several other sets of experimental data (under different operating conditions). The more popular multi-component LDF model is also tuned on the same data, but the model predictions do not match experimental data as well. Since the computational time is almost the same for the two models, the rigorous model is recommended for use. (c) 2006 Elsevier Ltd. All rights reserved.