Based on the assumptions of uncoupled diffusion fluxes and loading-independent Fick diffusivities, the linear driving force (LDF) model developed by Glueckauf finds widespread usage in the modelling of transient mixture uptake in microporous adsorbents. A number of experimental investigations report overshoots in intra-crystalline loadings of the more mobile species during transient binary mixture uptake in microporous adsorbents; these overshoots are not anticipated in the classic Glueckauf approach. The origins of the overshoots are traceable to strong coupling between species transfers engendered by mixture adsorption equilibrium thermodynamics; such coupling effects are most conveniently described by the Maxwell-Stefan (M-S) diffusion formulation. In this article, an explicit analytic model is developed to calculate transient mixture uptakes by combining the Maxwell-Stefan formulation with the linearization procedure of Glueckauf. The Maxwell-Stefan-Glueckauf model is validated by comparison with six different experimental data sets. In all six cases, the overshoots in the uptake of the more mobile partner species are properly captured; the incorporation of this approach in practical design procedures for adsorbers is expected to result in significant reduction in model complexity and computational times.