In a fuel cell which has an activated carbon-containing anode and an activated carbon-containing cathode and is preferably used for the oxidative treatment of waste waters containing oxygen or oxygen-containing compounds, the cathode has been subjected to partial anodic oxidation in a mineral acid at a potential epsilon h of from +1.3 to +10V and then doped with molybdenum(VI) and/or tungsten(VI) and/or vanadium(V) compounds, and the anode has been subjected to partial anodic oxidation in an aqueous mineral acid, cathodically reduced in an aqueous mineral acid and then impregnated with cobalt hydroxide and/or nickel hydroxide and/or copper hydroxide and/or zinc hydroxide, the anode and the cathode being separated by a porous polyelectrolyte through which the waste water flows.