A process and an apparatus control output of an air-breathing fuel cell system which consists of an air supply line, a fuel cell, an air exhaust line, and a separate gas supply system for hydrogen gas. To control the fuel cell output, an adjustable rotary speed compressor is located in the air supply line and a variable absorption capacity expander is located in the air exhaust line. The compressor, the expander, and an additional electric motor are positioned on a common shaft. The expander converts the pressure energy contained in the exhaust air into mechanical energy and delivers that energy via the common shaft to the compressor. The air volume flow is controlled by the compressor rotary speed and adjusted to a preset value. A preset working pressure is established in the fuel cell system by adjusting the absorption capacity of the expander.