A fuel injection system for multi-cylinder internal combustion engines, which has one injection unit per cylinder. Each injection unit includes one injection valve, one control valve, one flow limiting valve and one injection nozzle and is supplied with fuel via a fuel delivery line. Each injection unit also has a control unit which actuates the applicable control valve. This actuated control valve then actuates the associated injection valve, which in turn opens the fuel delivery line upstream of the injection nozzle. The flow limiting valve disposed upstream of the injection valve in the fuel delivery line blocks fuel flow when the fuel quantity flowing through the flow limiting valve attains a maximum fuel quantity, and the flow limiting valve does not open again until the fuel delivery line is blocked downstream of the flow limiting valve. To improve this system, each injection unit is assigned a sensor, with which a leak downstream of the flow limiting valve can be indicated; the control unit increases the injection duration, for the cylinder affected by a leak, enough though the correlated fuel quantity is greater than the maximum fuel quantity.