The kinetics of adsorption and desorption for an adsorbent particle, subjected to a step change in surface concentration, have been analyzed in detail for isothermal diffusion-controlled systems in which the diffusivity increases strongly with loading. The transient adsorption curves retain the same shape as for a constant diffusivity system, even when the diffusivity varies by more than an order of magnitude. The effective diffusivity increases with the size of the concentration step and depends on both the diffusivity ratio (between final and initial values) and the form of the concentration dependence. When the diffusivity ratio is high the desorption rate also increases with step size but by a much smaller factor. For very high diffusivity ratios (more than an order of magnitude) the shape of the desorption curves changes showing a much slower final approach to equilibrium than for a constant diffusivity system. A simple model is developed for such systems leading to a simple analytic expression for the desorption curve. The theory is validated by comparison with representative experimental data and used to explain some of the apparent anomalies in previously published studies. (C) 2004 Elsevier Ltd. All rights reserved.