A system, which is used in particular as a fuel injection system for the high-pressure injection in internal combustion engines, includes a fuel distributor and a plurality of fuel injectors. Each fuel injector is situated on a cup of the fuel distributor. At least one of the fuel injectors is fastened to the associated cup by a holding element, which has a supporting surface. The cup has a contact surface on an underside, by way of which the cup is supported at the supporting surface of the holding element by a damping layer. The holding element is attached to the cup. In addition, the fuel injector has a collar, which is braced on the holding element. Because of the damping layer, vibrations are able to be dampened, and the noise transmissions is able to be reduced.