Bearing for extremely high speed shafts of screw compressors consisting of a cylindrical roller bearing to take up the radial forces and a pair of inclined ball bearings to take up the axial forces, with the bearings arranged in a housing. One of the inclined ball bearings (30') acts as a pressure bearing and is designed with a contact angle alpha in the region between 30 deg. and 40 deg. and the second inclined ball bearing (32') serves as a support bearing and has a contact angle beta which is smaller than the angle alpha, in the region between 15 deg. and 25 deg. USE/ADVANTAGE - Bearing in which the internal forces resulting from the centrifugal force effect are small, allowing induced axial forces in the system to be considerably reduced.