A fuel cell system with a reformer for generating hydrogen-containing synthesis gas and a fuel cell of the fuel cell system. The fuel cell is arranged downstream of the reformer. The fuel cell system is heated up conventionally in a first heat-up phase by combusting a superstoichiometric fuel/air mixture. The first heat-up phase is stopped by stopping the combustion of the fuel/air mixture in the mixing chamber of the reformer. In a second heat-up phase, in which the reformer catalyst is operated in the catalytic combustion operation with a superstoichiometric fuel/air mixture, the entire heat-up process can be significantly shortened by a change in stoichiometry at the end of the second heat-up phase.