The time-lag and the diffusional conductance of a two-layer hollow cylindrical membrane have been calculated and measured in terms of the time-lags and conductances associated with the individual layers. The solubility of diffusant in each lamina was assumed to obey Henry's law and the diffusion coefficient in each lamina to be either a constant or a separable function of both distance and time (non-Fickian diffusion). The experimental membrane consisted of an inner sheath of nylon surrounded by one of polyethylene. Experiments on each component sheath produced evidence of non-Fickian diffusion (time-dependence of D) in polyethylene but not in nylon. Nevertheless, reasonable agreement was obtained between experimental time-lags for the laminate and those calculated neglecting this time-dependence, for diffusion of He, Ne, Ar, H2 and CO2 between 10 and 60°C.