Abstract: Multistage centrifugal compressor provided with a shaft with blades, which is mounted in a housing with bearings. At least one bearing is provided with a bearing damper element including a ring arranged between the shaft and the bearing. The ring includes slots through the thickness of the ring in the axial direction (X-X?) and at a distance from the radially-directed inner and outer surface of the ring. The slots are at least partially overlapping, and: A) the slots are filled with a liquid, and the axial annular surfaces are closed off by means of a protective cap; or: B) at least one of the annular surfaces is provided with a viscoelastic material or hysteretic damping material sandwiched between two concentric discs, which discs are attached to the ring; or: C) the slots are filled with a viscoelastic material.