The diffusion process of toluene in polystyrene films is investigated in the vicinity and slightly above the glass-transition of the mixture. A detailed analysis investigates whether the diffusion follows Fick's law or other effects are superimposing the mass transport process. For that purpose, the diffusion of toluene in polystyrene films of different thicknesses at otherwise constant conditions was observed by gravimetric sorption measurements. Even slightly above the glass-transition of the toluene-loaded polymer a remaining influence of the polymer relaxation on the diffusion process (non-Fickian diffusion) is observed. The diffusion Deborah number concept was applied using an experimentally independent relaxation time for the polystyrene-toluene mixture. The results show quantitatively the same trend but finally deviate by about 1 order of magnitude.