In a unit fuel injector for pilot and main injection, the yielding piston interacts with a hydraulic damping member and a stop shoulder of the nozzle needle interacts with a spatially fixed offset. In order to achieve a better injection characteristic under all operating conditions, the yielding piston is short and light and the pressure stud of the nozzle needle forms a restriction opening with the spatially fixed offset. The yielding piston can have a guide projection with grooves and variable damping in the course of its stroke. The damping of the valve needle can furthermore be modulated. <IMAGE>
