A cylinder-piston unit, with at least one cylinder accommodating an injection solution, at least one piston, and an adhesive coating arranged in the area of the free end face of the cylinder. The cylinder has a bottom portion, on which a discharge tube is arranged. An adhesive disc, which is displaceable in the direction of the centre line of the cylinder-piston unit between an installation position and an application position, is arranged on the discharge tube and/or on the bottom portion. On its end face directed away from the bottom portion, the adhesive disc has an adhesive coating. In the storage position, the adhesive disc has at least one sealing element or a sealing area for closing the discharge tube, the effect of which sealing element or sealing area is no longer present in the application position. In the application position, the front edge of the end face of the discharge tube protrudes at least 0.5 mm beyond the adhesive coating of the adhesive disc. A cylinder-piston unit of an injector is developed whose discharge system is suitable for safely penetrating the outer layers of skin, covered by the term “dermis”, in order to convey the injection solution into or under the skin and keep it there for a definable period of time.