A method is described for the electrolysis of an aqueous solution of hydrogen chloride or alkali metal chloride in an electrolysis cell. The cell includes at least of an anode half-element and an anode, a cathode half-element and a gas diffusion electrode as the cathode, and a cation exchange membrane for separating the anode half-element and the cathode half-element. A gas containing oxygen is supplied to the cathode half-element and excess gas containing oxygen is discharged from the cathode half-element. Excess gas containing oxygen discharged from the cathode half-element is subjected to catalytic oxidation of hydrogen.