A fuel-cell system, particularly a drive system for a motor vehicle, includes an autothermal reformer unit for producing hydrogen from a raw material in order to operate a downstream fuel cell unit. An oxidation device for converting carbon monoxide into carbon dioxide is arranged between the reformer unit and the fuel-cell unit. The fuel-cell system further includes a two-stage compressor, which supplies a first pressure to a cathode of the fuel cell unit by a first stage and supplies a second pressure to the reformer unit by a second stage.