One of the primary requirements for commercialization of hydrogen fuel-cell vehicles is the on-board storage of hydrogen in sufficient quantities. On-board storage of hydrogen by adsorption on nano-porous adsorbents at around liquid nitrogen temperatures and moderate pressures is considered viable and competitive with other storage technologies: liquid hydrogen, compressed gas, and metallic or complex hydrides. The four cryo-adsorber fuel tank processes occur over different time scales: refueling over a few minutes, discharge over a few hours, dormancy over a few days, and venting over a few weeks. The slower processes i.e. discharge, dormancy and venting are expected to have negligible temperature gradients within the bed, and hence are amenable to a lumped-parameter analysis. Here we report a quasi-static lumped-parameter model for the cryo-adsorber fuel tank, and discuss the results for these slower processes. We also describe an alternative solution method for dormancy and venting based on the thermodynamic state description. (C) 2009 International Association for Hydrogen Energy. Published by Elsevier Ltd. All rights reserved.