Properties of porous, single-crystal membranes have been modelled for Langmuir's isotherm assuming that entry to and exit from the crystal proceeds via an externally adsorbed layer. The potential moderating role of surface processes upon steady flow depends strongly upon temperature and upon the difference in activation energy for escape from the crystal to the externally adsorbed layer and that for intracrystalline diffusion. The moderating role decreases with increasing membrane thickness. Where steady flow is reduced by surface processes the apparent diffusivity found from this flow is less than the true intracrystalline diffusivity by an amount which increases the smaller the crystal. If along one-dimensional channel systems there are occasional partial blockages with associated abnormally high energy barriers, quantitative extension of the model shows potentially large flow reductions, independent of membrane thickness. Provided surface processes have in comparison a negligible effect steady flow will give the correct average intracrystalline diffusivity. Mixture separation has been considered in partially blocked or unblocked crystal membranes in the Henry's law range.