The dynamics of bidisperse pore pressurization with multicomponent mixtures is studied using the Maxwell-Stefan approach to describe the mass-transfer processes in macro- and micropores; The solid network is described by the branched micropore-macropore model, allowing for adsorption to occur at both levels. The adsorption equilibrium is described with the extended Langmuir isotherm. Numerical solutions of partial pressure and surface coverage profiles are obtained using orthogonal collocation in finite elements. The effects of micropore surface diffusivity and feed composition on the controlling resistance for the separation of a binary mixture of inert and adsorbable gases are studied, A criterion is suggested for identification of the controlling resistance that takes into account the effect of composition on convective transport and micropore surface diffusion. The effect of macropore resistance on a kinetics-based separation is analyzed for a binary mixture of two adsorbable components. The separation of a ternary mixture is also addressed, in a study of the effects of the inert gas concentration in the feed on the system dynamics for a mixture of an inert and two adsorbable gases with different affinities.