A gap seal device includes a housing with a fluid-filled guiding chamber and a multi-part piston that is translationally and/or rotationally moveable in the guiding chamber. The piston separates a high-pressure region from a low-pressure region of the guiding chamber. The piston forms an annular gap having a nominal gap width with an inner wall delimiting the guiding chamber. The piston has a stepped rod, a sleeve, which is slipped over a stepped-down region of the rod and which has a blind hole, and a coupling. The stepped-down region of the rod or in a tube portion of the sleeve includes a stiffness change. A gap width of the annular gap that is reduced compared with the nominal gap width can be set in a region radial to the stiffness change by stress-caused expansion of an outside diameter of the tube portion of the sleeve in accordance with the set stressing force.