NOVELTY - The method of operating a hydrogen generator, comprises stopping supply of a source material and water to a reformer (101) in a stop operation period, operating a carbon monoxide reduction heater such that a temperature of a carbon monoxide reducing portion is kept higher than a first predetermined temperature, supplying the source material to purge an interior of the hydrogen generator when the temperature detected by a reformer temperature sensor (105) becomes a temperature that fails to allow carbon to be deposited on a reforming catalyst, and stopping the supply of the source material.    USE - The method is useful for operating a hydrogen generator, which is useful in a fuel cell system (claimed).    ADVANTAGE - The method is capable of efficiently, reliably and safely operating the hydrogen generator to inhibit condensation of water within the carbon monoxide reducing portion during the stop operation period thus avoiding the deterioration of the catalyst.    DETAILED DESCRIPTION - The method of operating a hydrogen generator, comprises stopping supply of a source material and water to a reformer (101) in a stop operation period, operating a carbon monoxide reduction heater such that a temperature of a carbon monoxide reducing portion is kept higher than a first predetermined temperature, supplying the source material to purge an interior of the hydrogen generator when the temperature detected by a reformer temperature sensor (105) becomes a temperature that fails to allow carbon to be deposited on a reforming catalyst, and stopping the supply of the source material and the operation of the carbon monoxide reduction heater. The first predetermined temperature fails to allow steam present within the carbon monoxide reducing portion to condense. The reformer, a unit (104) to heat the reformer, the carbon monoxide reducing portion, the carbon monoxide reduction heater, and the reformer temperature sensor are present on the hydrogen generator. The reformer includes a catalyst to cause the source material and water to react with each other to generate a hydrogen-rich reformed gas. The carbon monoxide reducing portion comprises a shifter and a carbon monoxide removing portion. The carbon monoxide reduction heater comprises a shifter heater and a carbon monoxide removing portion heater. The shifter has a carbon monoxide reducing catalyst comprising a shift reaction catalyst. The carbon monoxide removing portion has a catalyst comprising a selective oxidization catalyst and a methanation catalyst. In the stop operation period, the carbon monoxide reduction heater is operated in response to a stop instruction and for a time period during which the temperature of the carbon monoxide reducing portion is not higher than the first predetermined temperature to initiate a stop operation. The hydrogen generator further includes a first- and a second purge gas supply portion to supply a first purge gas and a second purge gas such as air respectively. The first purge gas supply portion is operated until the temperature detected by the reformer temperature sensor becomes lower than the second predetermined temperature, when the temperature detected by the reformer temperature sensor is not lower than the second predetermined temperature. The second purge gas supply portion is operated until the hydrogen generator becomes fully filled with the second purge gas when the temperature detected by the reformer temperature sensor is lower than a second predetermined temperature. The second predetermined temperature is a temperature that fails to allow the reforming catalyst to be oxidized. The first purge gas is steam, or one of a combustion exhaust gas and an inert gas. An INDEPENDENT CLAIM is included for a method of operating a fuel cell system.    DESCRIPTION OF DRAWING(S) - The figure shows a block diagram of a configuration of a hydrogen generator.    Reformer (101)    Material supply portion (102)    Water supply portion (103)    Reformer heater unit (104)    Reformer temperature sensor. (105)