NOVELTY - The method comprises supplying a fuel cell assembly including a cathode (14) and an anode (12) with an electrolyte, supplying a concentrated (20 M) solution of a liquid fuel to the anode and an oxidant to the cathode, and operating the fuel cell assembly at a low oxidant stoichiometry epsilon c of less than 2.5, a steady-state power density of greater than 70 mW/cm2 and a temperature of 60 degrees C. The cathode comprises a gas diffusion medium including a backing layer and a microporous layer, a catalyst layer, and a hydrophobic microporous layer.    USE - The method is useful for operating a direct oxidation fuel cell system, which is useful in portable and mobile applications such as notebook computers, mobile phones and personal data assistants.    ADVANTAGE - The method ensures effective operation of a direct oxidation fuel cell system at low oxidant stoichiometries, a steady-state power density and desired temperature with high power efficiency without flooding, provides easy storage/handling of the cell system and high energy density of the liquid fuel, and maintains a net water balance in the cell, where the total water loss from the cell through the cathode does not exceed the net production of water.    DETAILED DESCRIPTION - The method comprises supplying a fuel cell assembly including a cathode (14) and an anode (12) with an electrolyte, supplying a concentrated (20 M) solution of a liquid fuel to the anode and an oxidant to the cathode, and operating the fuel cell assembly at a low oxidant stoichiometry epsilon c of less than 2.5, a steady-state power density of greater than 70 mW/cm2 and a temperature of 60 degrees C. The cathode comprises a gas diffusion medium including a backing layer and a microporous layer, a catalyst layer, and a hydrophobic microporous layer. The microporous layer comprises an electrically conductive material and a fluoropolymer (5-30 wt.%). The electrically conductive material comprises 0.5-5 mg/cm2 of carbon particles or nanofibers. The microporous layer has a thickness of 10-50 mu m and an average pore size of 10-500 nm. The backing layer comprises carbon paper or woven or non-woven cloth having a porosity of greater than 70%. The catalyst layer, the hydrophobic microporous layer, and the gas diffusion medium are arranged in overlying sequence in the recited order. The liquid fuel is methanol. The oxidant is air.    DESCRIPTION OF DRAWING(S) - The figure shows a simplified schematic view of a direct oxidation fuel cell system capable of operating with highly concentrated methanol fuel system.    Membrane electrode assembly (9)    Direct methanol fuel cell system (10)    Anode (12)    Cathode (14)    Cartridge (18)    Fan. (20)