Exchange diffusion experiments of the exchanging ion pairs Cl-/Br- and Cl-/SO42- in an anion exchange membrane and of Na+/H+ in three cation exchange membranes have been carried out using a dialysis cell. The time dependent concentrations in the cell are measured with precision densimetry based on the principle of the vibrating tube. Thermodynamic ion exchange equilibria between the membrane phase and the electrolyte solution have also been measured for the three systems Cl-/Br-, Cl-/SO42-, and Na+/H+ using atomic absorption spectrometry and ion chromatography as analytical methods. The experimental data of exchange diffusion and exchange equilibria are used to study the diffusion velocity of the mobile ions in the membrane on the basis of the Maxwell-Stefan formalism of multicomponent diffusion processes. In frame of the solution-diffusion model equations are derived for the ion exchange diffusion process which allow to determine diffusion coefficients of the exchanging ions in the membrane and which account also for frictional effects between the ions expressed by a coupling diffusion coefficient. The method developed can generally be applied to study transport processes in electromembrane systems.