A general expression has been obtained for the time-lag in transport through membranes. based only on the conservation of mass condition and independent of any assumed equation of flow. When considered in relation to Fick's equation the time-lag expression covers all situations in which diffusion coefficients, D, are functions of concentration, distance or time, or combinations of these variables. When D is a function only of concentration, C, two new ways have been given for exact treatments of the time-lag. These avoid difficulties which arise in using the formula originally given by Frisch (1957) and previously used in time-lag studies. Differences can arise between time-lags where D is a function only of C and the time-lag L given by the general equation. These differences serve for the study of non-Fickian diffusions in which D is a function also of distance or time. This treatment, applied to a number of microporous membranes, leads to the conclusion that in these membranes non-Fickian components sometimes arise which are mostly dominated by time-dependence in the overall diffusion coefficient. It is shown how this behaviour can result from the partial blind-pore character of the channels in the membranes. In this and other ways the time-lag has been shown to give information about micropore systems which is not readily found from other measurements.