NOVELTY - Operation of a fuel cell comprises controlling a number of moles of oxygen contained in air supplied to air electrode, by keeping the number of moles of oxygen at level of less than or equal to one half of a number of moles of hydrogen contained in the fuel supplied to the fuel electrode, or a number of moles of unreacted hydrogen contained in the fuel discharged from the fuel electrode, at a level equal to or greater than a predetermined value.    USE - For operation of a fuel cell for a fuel cell power generation device, useful for fuel cell power generation system (claimed).    ADVANTAGE - Life of fuel cell is prolonged.    DETAILED DESCRIPTION - Operation of a fuel cell in which unit cells are stacked, each of the unit cells including a fuel electrode to which a fuel containing hydrogen as a major component is supplied, an air electrode to which air is supplied as an oxidizing agent, and an electrolyte provided between the fuel electrode and air electrode, comprises controlling a number of moles of oxygen contained in the air supplied to the air electrode, by keeping the number of moles of oxygen at level of less than or equal to one half of a number of moles of hydrogen contained in the fuel supplied to the fuel electrode, or a number of moles of unreacted hydrogen contained in the fuel discharged from the fuel electrode, at a level equal to or greater than a predetermined value. INDEPENDENT CLAIMS are also included for:    (a) a fuel cell power generation device, comprising a fuel cell; hydrogen supply measurement mechanism; and oxygen supply control mechanism for controlling a number of moles of oxygen contained in the air supplied to the air electrode, based on data measured by the hydrogen supply measurement mechanism, where hydrogen supply measurement mechanism measures a number of moles of hydrogen contained in the fuel supplied to the fuel electrode, or a number of moles of unreacted hydrogen contained in the fuel discharged from the fuel electrode; and    (b) a fuel cell power generation system comprising a firing furnace, which includes combustion mechanism for producing a combustion gas by burning a fuel containing methane, and a firing furnace body, which fires a firing target substance carried in it, by the combustion gas; a reformer, which is filled with a methane reforming catalyst, causes a reformation raw material including the fuel containing methane and steam entering the reformer to come in contact with the methane reforming catalyst, while heating the raw material to cause the methane and the steam in the reformation raw material to react, producing a reformed gas containing hydrogen and carbon dioxide; and a fuel cell power generation device comprising a fuel cell, where reformed gas containing hydrogen is produced by the reformer by using exhaust heat of the combustion gas produced by the firing furnace body, electricity is generated by using the reformed gas as the fuel for the fuel cell, and an unreacted reformed gas discharged from the fuel cell is burnt as the fuel for the combustion mechanism, utilizing the reformed gas containing hydrogen and converting a part of thermal energy of the combustion gas into electric energy    .    DESCRIPTION OF DRAWING(S) - The figure shows a schematic configuration diagram showing a fuel cell power generation system.