Time lag permeation experiments have been traditionally conducted with weakly adsorbing species or at low upstream concentrations, in order to simplify the asymptotic solution of the mass balance equations. In this paper, the solution is obtained for the case of non-linear adsorption according to the Freundlich and Langmuir isotherms and concentration dependent surface diffusion described by the model proposed by Yang et al. (1973, A.I.Ch.E. J. 19, 1052). This asymptotic solution is compared to the one obtained for the D-R isotherm with the concentration dependence of the surface diffusion coefficient represented by the gradient in chemical potential. The solutions are applied to the permeation data of Ash et al. (1963, 1973, Proc. R. Soc. A275 and A271, 1 and 255). The parameters and relations obtained are compared to those previously obtained from experiment with good agreement.