Properties of CMV cation exchange membranes used for electrodialysis of sulfuric acid solutions were investigated. Membrane characterization has led to determine the ion-exchange capacity and the hydrogen ion transport number in sulphuric acid media. The membrane electrical conductivities were measured as a function of the acid concentration. These data were used to check the applicability of the micro-heterogeneous model which describes the inner membrane microstructure as consisting of a joint gel phase and an interstitial phase. The derived value of the interstitial phase volume fraction is large (20%). This value has been correlated to the membrane water content in terms of a model taking into consideration the molecular conformation of polyvalent (polystyrene sulfonate) macro-ions located in the joint gel phase. The behaviour of membranes placed respectively in their acid and salt forms have been studied and discussed. In the interpretation of membrane swelling and acid absorption, emphasis has been put on the role of polyelectrolyte morphological modifications as a function of the concentration in the equilibrating solutions. The overall membrane homogeneity has been tested by using chronopotentiometric measurements at different current densities.