Diffusion coefficients of the aromatic compounds phenol, aniline, 2-chlorophenol, 4-nitrophenol, 2,4-dinitrophenol, 4,4＇-isopropylidenediphenol (Bisphenol A) and pyridine in dense polyether-polyamide block-copolymer (PEBA) 4033-PE and PEBA 4033 membranes have been measured using the technique of the time-dependent dialysis in dilute aqueous solution. A new evaluation procedure is presented which allows to determine diffusion coefficients in case of an nonstationary dialysis process. Diffusion coefficients obtained at 298.15 and 323.15 K are used to determine the so called activation energy of diffusion. The data are obtained in membranes used under realistic conditions of pervaporation or reverse osmosis where the polymer membrane is saturated to ca. 1% with water. The method is generally useful for estimating parameters of membrane separation processes in a quantitative way based on the solution diffusion model.