An analytical solution is given to the problem of transport through a slab membrane in the presence of two simple boundary-layer resistances and explicit expressions derived for the time-lags associated with the permeation. The treatment relates to a constant diffusion coefficient. Calculated values of the outgoing 'adsorption' time-lag differ markedly from those obtained by Skaarup and Hansen [Polym. Eng. Sci. 20 (1980) 259] using a numerical procedure. Use of four time-lags allows the solubility/adsorption isotherm to be determined.