An apparatus for the continuous electrochemical desalination of aqueous solutions includes a wound module having a central electrode, around which are wound an anion exchanger membrane and a cation exchanger membrane, and an outer counterelectrode. Each membrane is sealed at an inner edge thereof and at a outer edge by a respective clamping device, or are anchored in a synthetic resin block, in such a way that a dilution chamber and a concentrate chamber are defined. The dilution chamber and/or the concentrate chamber may contain an ion exchanger resin. The central electrode and the outer counterelectrode each may have a constriction over at least a part of the circumference thereof. The central electrode may furthermore have a recess for receiving the inner clamping device or the inner synthetic resin block in order to achieve a winding having as spiral a cross section as possible.