NOVELTY - A redox fuel cell (1) comprises anode, cathode (3), unit for supplying fuel, unit for supplying an oxidant, unit for providing electrical circuit between the electrodes, and catholyte solution comprising redox mediator which is partially reduced at the cathode in operation of the cell, and partially regenerated by, optionally indirect, reaction with the oxidant after the reduction. The catholyte solution comprises complexed multidentate N-donor ligand as redox mediator and/or as redox catalyst catalyzing the regeneration of the mediator.    USE - Redox fuel cell. Uses include but are not limited to portable electronic products, automobiles, caravans, recreational vehicles, boats, hospital computer power supply, domestic power supply and business application power supply.    ADVANTAGE - The redox fuel cell has higher potential and higher sustainable current. The catholyte enables to design catholyte system efficiently.    DETAILED DESCRIPTION - A redox fuel cell comprises an anode and a cathode separated by an ion selective polymer electrolyte membrane, unit for supplying fuel to the anode region, unit for supplying an oxidant to the cathode region, unit for providing electrical circuit between the electrodes, and catholyte solution comprising non-volatile catholyte component(s) flowing in fluid communication with the cathode. The catholyte solution comprises a redox mediator which is partially reduced at the cathode in operation of the cell, and partially regenerated by, optionally indirect, reaction with the oxidant after the reduction. The catholyte solution comprises complexed multidentate N-donor ligand as redox mediator and/or as redox catalyst catalyzing the regeneration of the mediator. The ligand comprises heterocyclic substituent(s) chosen from pyrrole, imidazole, 1,2,3-triazole, 1,2,4-triazole, pyrazole, pyridazine, pyrimidine, pyrazine, indole, tetrazole, quinoline, isoquinoline (all optionally substituted by alkyl, alkenyl, aryl, cycloalkyl, alkaryl, alkenaryl, aralkyl and/or aralkenyl groups). INDEPENDENT CLAIMS are included for the following:    (1) catholyte for use in a fuel cell; and    (2) method for operating a proton exchange membrane fuel cell, which involves forming hydrogen ions at anode adjacent to proton exchange membrane, supplying the catholyte with its redox mediator in an oxidized state and its redox catalyst in a reduced state to cathode oppositely adjacent to the membrane, and allowing the mediator to become reduced upon contact with the cathode concomitantly with hydrogen ions passing through the membrane to balance charge.    DESCRIPTION OF DRAWING(S) - The drawing shows the schematic view of cathode compartment of a fuel cell.    Redox fuel cell (1)    Polymer electrolyte membrane (2)    Cathode (3)    Oxidant inlet (4)    Cathode gas reaction chamber (5)