Abstract: The invention relates to the dry run-high pressure stage of a multistage piston compressor with a piston designed as a tappet (2) guided in the high pressure cylinder (1) and sealed against the compression space of the cylinder (1) by means of self-lubricating sealing elements (3) forming an annular gap together with the working surface, whereby the latter is formed by a material suitable for dry run. According to the invention, the sealing elements having a height conforming at least to their diameter are embodied in the form of at least two cylindrical sealing elements (3), which are loosely placed one on top of the other in the cylinder (1) on the free end of the tappet (2), provided with working surface guides at least in part areas, and have chamfers (6) on the face side.