NOVELTY - The method comprises introducing a catalyst carrier into a reactor (99), where catalysts are applied on the catalyst carrier by coating or impregnating the catalyst carrier for the catalysis of reformation reaction and water gas shift reaction, producing two zones having axial temperature distribution in the catalyst carrier, and guiding gaseous/evaporatable educt gases containing hydrocarbon through a first zone and then through second zone of the catalyst carrier. The reformation reaction predominantly runs in the first zone with minimum temperature above the temperature of the second zone.    USE - Method for producing hydrogen-containing gas mixture useful in an integrated fuel cell system (claimed), which is useful in the automotive industry.    ADVANTAGE - The method ensures economical, simple and efficient production of the hydrogen-containing gas mixture with low carbon monoxide concentration, high quality and less effort.    DETAILED DESCRIPTION - The method comprises introducing a catalyst carrier into a reactor (99), where catalysts are applied on the catalyst carrier by coating or impregnating the catalyst carrier for the catalysis of a reformation reaction and a water gas shift reaction, producing two zones having axial temperature distribution in the catalyst carrier, and guiding gaseous or evaporatable educt gases containing hydrocarbon through a first zone and then through a second zone of the catalyst carrier. The reformation reaction predominantly runs in the first zone with a minimum temperature above the temperature of the second zone and the water gas shift reaction predominantly runs in the second zone with a maximum temperature below the temperature of the first zone. The reformation reaction consists of steam reformation, catalytic partial oxidation and autothermal reformation reaction. The temperature distribution is produced by active or passive heat exchanger principle. The catalyst is present as filling. The catalyst carrier is present in the form of honeycomb, foam, non-woven and/or lattice, and is present as circular honeycomb (1) and/or complete honeycomb. A gas entry temperature at the first zone is 600-950 degrees C and the gas entry temperature at the second zone is 150-350 degrees C. INDEPENDENT CLAIMS are included for:    (1) a reactor for producing hydrogen-containing gas mixture; and    (2) an integrated fuel cell system.    DESCRIPTION OF DRAWING(S) - The diagram shows a schematic representation of a reactor.    Circular honeycomb (1)    Reactor tube (4)    Lower Flange (20)    Upper Flange (21)    Reactor. (99)