NOVELTY - The method comprises producing hydrogen from an exothermic reaction of water with an additive (Z), and heating an exhaust gas (A) at cathode exit side of a fuel cell (1) guided into an exhaust gas channel (2) based on the reaction heat developed during the exothermic reaction. The water and the additive bound in the exhaust gas are supplied to a reactor (3), which contains catalytic material, and exothermally reacts in the exhaust gas channel. The non-reacted water is supplied to a first container (7). The by-product of the exothermic reaction is supplied to a second container (8).    USE - Method for generating hydrogen in a fuel cell system of a vehicle.    ADVANTAGE - The method is capable of effectively and continuously generating the hydrogen in the fuel cell system with high capacity.    DETAILED DESCRIPTION - The method comprises producing hydrogen from an exothermic reaction of water with an additive (Z), and heating an exhaust gas (A) at cathode exit side of a fuel cell (1) guided into an exhaust gas channel (2) based on the reaction heat developed during the exothermic reaction. The water and the additive bound in the exhaust gas are supplied to a reactor (3), which contains catalytic material, and exothermally reacts in the exhaust gas channel. The non-reacted water is supplied to a first container (7). The by-product of the exothermic reaction is supplied to a second container (8). The produced hydrogen and by-products (N) of the exothermic reaction are separated from each other during the exothermic reaction of the non-reacted surplus water contained in the exhaust gas. The non-reacted water during the exothermic reaction is supplied to a new exothermic reaction, to a flow input side of the reactor and/or the exhaust gas channel. The hydrogen produced during the exothermic reaction is supplied to the fuel cell at the anode input side. During the exothermic reaction, high water conversion and large reaction heat are produced, so that an emission of liquid water from the exhaust channel is prevented. An INDEPENDENT CLAIM is included for a device for generating hydrogen in a fuel cell system of a vehicle.    DESCRIPTION OF DRAWING(S) - The diagram shows a schematic view of a device for generating hydrogen in a fuel cell system of a vehicle.    Fuel cell (1)    Exhaust gas channel (2)    Reactor (3)    Separating device (4)    First container (7)    Second container. (8)