TECHNOLOGY FOCUS - CHEMICAL ENGINEERING - Preferred Condition: Reformate comes out of the selective oxidation catalyst section.Preferred Catalyst: The combustion catalyst is capable of combusting the hydrocarbon-based fuel or hydrogen.Preferred Method: In the first combustion step, imperfect combustion is caused to occur by supplying combustion air so that an air ratio results to be smaller than one; and in the second combustion step, the fuel that has been imperfectly combusted in the first combustion step is combusted perfectly by supplying combustion air so as to result in the air ratio that permits perfect combustion to occur. Extinction is caused to occur in the first combustion step by increasing the flow rate of combustion air or by decreasing the flow rate of the combustion fuel containing the fluid(s), stopping the first combustion step and starting the second combustion step. In the second combustion step the combustion fuel containing the fluid(s) is combusted using the combustion catalyst; and the supply of the combustion fuel is halted, the supply of the combustion air is maintained, the supply of the combustion fuel containing the fluid(s) is supplied again, and the first combustion step is started.    TECHNOLOGY FOCUS - MECHANICAL ENGINEERING - Preferred Apparatus: The fuel processing apparatus further comprises a catalyst combustion air supply section for supplying combustion air for the combustion catalyst to the upstream side of the combustion catalyst section in the combusted exhaust gas passage.Preferred Component: The combustion catalyst section has an outlet for the combusted exhaust gas to come out; and a combustion catalyst temperature detecting section (31, 32, 33) disposed at the outlet to detect the temperature of the combustion catalyst.    TECHNOLOGY FOCUS - ORGANIC CHEMISTRY - Preferred Component: The combustion fuel comprises fluid(s) comprising an anode off-gas produced in a step of generating electricity using reformate having undergone the selective oxidation step; and/or a hydrocarbon-based fuel (preferably a hydrocarbon-based fuel).