A fuel injection system has one or more unit fuel injectors or pump-line-nozzle units, corresponding in number to the cylinders, for compressing the fuel. The fuel injection system includes means for generating two different injection pressures during the injection and at least one valve for controlling the injection with a cross sectional control. The fuel injection with the aid of the unit fuel injector or a pump-line-nozzle unit can be achieved over a wide rpm range with great precision.