METHOD FOR OPERATING A MULTI-STAGE AIR COMPRESSION SYSTEM, MULTI-STAGE AIR COMPRESSION SYSTEM, AND FUEL CELL SYSTEM

The invention relates to a method for operating a multi-stage air compression system () comprising an electrically driven first compressor () and a second compressor () driven by a turbine (), wherein the compressors () are arranged in a supply air path () and the turbine () is arranged in an exhaust air path () of an air system for supplying air to a fuel cell stack (). According to the invention, when the air compression system () is started, the air compressed by means of the first compressor () is supplied to the fuel cell stack () via a bypass () to bypass the second compressor () and the second compressor () is connected to the surrounding environment on both the inlet and outlet sides via at least one valve () and/or a throttle valve (). The invention further relates to a multi-stage air compression system () as well as a fuel cell system having a multi-stage air compression system ().