A fuel cell system includes a fuel cell unit and a gas-generating system containing at least one reforming unit for obtaining a hydrogen-rich reformate from a fuel. It is possible to supply the reformate at least partly to the anode side of the fuel cell unit. The system may include a first reforming reactor for producing a first reformate with a high outlet temperature; a second reforming reactor for producing a second reformate with a second outlet temperature which is below the first outlet temperature; a mixing element for mixing the first reformate with at least one fuel and located between an outlet of the first reforming reactor and an inlet of the second reforming reactor. The second reformate may be supplied to a gas-purification system and the purified reformate supplied to the fuel cell unit.