Abstract: Bearing system for a rotor of an electric machine having an outer rotor part formed as a hollow cylinder and an inner rotor part disposed therewithin, the rotor having a drive side and an exciter side at opposite ends thereof, the inner rotor part being operatable in cryogenic temperature range and being fastened thermally insulatingly with respect to the outer rotor part, which is warmer relative to the inner rotor part, the inner rotor part being firmly flanged to the outer rotor part at the exciter side, the outer and the inner rotor parts having separate outer and inner coaxial shaft shanks supported so as to be movable thermally in axial direction independently of one another, an expansion compensator being disposed between the outer and the inner coaxial shaft shanks and serving also for sealing from the outside a hollow space formed between the inner and the outer rotor part, includes first and second separate shaft bearings with respective bearing boxes associated with the outer and inner shaft shanks