By extrapolation of the extensive use of cyclodextrin (CD)-modified materials in chromatography techniques, we study CD-containing membranes as contactors having facilitated transport properties in liquid/liquid extraction. Our main interest lies in the understanding and modelling of the mass transport mechanism for the development of pertraction applications using these membranes. The sorption and diffusion processes of xylenes as model molecules were studied through sorption experiments in membranes containing alpha-CD. The presence of highly pronounced induction times on sorption curves makes it impossible to use standard models, like the solution-diffusion one, to describe the experimental data. A generalized dual mode model has therefore been developed to account for three distinct regimes of strong facilitated transport membranes: (i) one controlled by diffusion within a membrane, (ii) one controlled by a kinetic retardation of solute entry into and out of a membrane, and (iii) one controlled by the kinetics of complexation formation. The permeant species are divided into two populations: one diffusing in the membrane and one forming immobile inclusion complexes with fixed CD sites. The model fits, which agree well with the experimental data using a limited number of adjustable parameters, indicate that the kinetics of interfacial transfer depends on the CD content.