A new general equation has been developed for the lag time for a dilute diffusant permeating through a one-dimensional membrane in which both diffusivity D and partition coefficient K are dependent on position. The lag time is given by tL=∫h0K(x)[∫x0 R(y)dy][∫hxR(y)dy] ×dx/ ∫h0R(x)dx, where h is the membrane thickness and R(x)=1/[D(x)K(x)]. Formulas derived from this equation include those for: lag time in the presence of an electrical potential gradient; lag time in a multilaminar periodic membrane; and an upper bound for lag time given by tL <(h2/ 4Deff), where Deff is the effective diffusivity as deduced from steady-state partitioning and permeability measurements. The lag time is shown to be independent of the direction of diffusion. A computational technique is presented in which the equation for tL is rearranged to a system of two differential equations, which are readily solvable by numerical integration, even when the system has discontinuities in D and K which would increase the difficulty of evaluating the double integral directly.