The invention relates to a fuel injection system (1) for an internal combustion engine in which fuel with at least two different fuel pressures can be injected by injectors (10) into the combustion chamber of an internal combustion engine comprising a central first pressure accumulator (6) for the higher pressure fuel and a central, second pressure accumulator (7) fed by the first pressure accumulator (6) wherein a lower fuel pressure is maintained, by regulating the fuel supply. A valve unit is provided for switching between the higher and lower fuel. The valve unit (12) for switching between the higher and lower fuel is provided locally for each injector (10). The injection system of invention enables improved dosing of the lower fuel pressure.