A new experimental methodology of studying the kinetics of water vapour sorption/desorption under operating conditions typical for isobaric stages of adsorption heat pumps has been proposed and tested experimentally in [Yu.I. Aristov, B. Dawoud, I.S. Glaznev, A. Elyas, A new methodology to study the kinetics of water vapour sorption/desorption under real operating conditions of adsorption heat pumps: 1. Experiment, Int. J. Heat Mass Transfer, submitted for publication]. Here, we analysed results obtained in [Yu et al., submitted for publication] by mathematical modelling of the coupled heat and mass transfer in a single adsorbent grain which is in thermal contact with a metal plate subjected to a fast temperature jump/drop (at constant vapour pressure). The dynamic behaviour turns out to be closely linked with equilibrium properties of the adsorbent, in particular, with the initial/final temperatures and with the shape of the segment of water sorption isobar (convex or concave) between these temperatures. (C) 2007 Elsevier Ltd. All rights reserved.