In the framework of solvent diffusion in glassy polymer films, this paper concerns an experimental study of sorption and desorption kinetics for a model system consisting of statistical PMMA/ PnBMA copolymer films of various composition. The experimental results are obtained by performing differential increasing and decreasing pressure steps, using a gravimetric technique based on a quartz crystal microbalance placed in a controlled solvent vapor pressure chamber. The non-Fickian behavior in the glassy state and the variations of the mutual diffusion coefficient with the solvent concentration on one hand and with the copolymer composition on the other hand are studied. Results are analyzed in terms of absolute solvent mass fraction (w(S)) and in terms of distance to the glass transition (w(S) - w(Sg)). This last representation highlights the prevailing part of the gap to the glass transition in the system under study.