Various aspects of the kinetics of sorption of acetone vapor by cellulose acetate films at 30 degrees C have been studied in detail, the principal aim being to understand more thoroughly the physical nature and causes of non-Fickian behavior in this and other similar polymer-micromolecular penetrant systems. Particular attention was given to the changes in sorption (including absorption, desorption, and resorption) kinetics caused by (a) systematic variation of the vapor pressure of acetone in different ways and (b) changes in membrane thickness. It has been shown that both viscous volume swelling relaxation and longitudinal differential swelling stress effects must be invoked, in order to explain fully the observed behavior. Detailed analysis of two-stage sorption kinetics indicated (1) reasonable agreement between estimates of the diffusion coefficient reported by different authors, as long as a consistent analysis of the first stage is used, although the significance of the values given is open to some doubt, because the said first stage is found not to be free of non-Fickian features; and (2) reasonable conformity of the second stage to a first-order volume relaxation process (except a long times), with a relaxation frequency strongly dependent on the width of the concentration interval covered by the sorption experiment (and hence on the applied "osmotic stress"). The close similarity of second-stage sorption to nonlinear viscoelastic creep behavior, previously found in the cellulose-water system was confirmed and is taken further here, by demonstrating semiquantitative agreement between the corresponding "elastic swelling" and mechanical bulk moduli.