An open-end rotor spinning machine which operates at rotor speeds higher than 100,000 rpm is constructed so that the critical system rotational speed is higher than the 100,000 rpm operating rotational speed. The rotatable rotor has a shaft bearingly supported in the nip between at least two pairs of supporting disks. Each disk has a plastic outer covering around the circumferential surface thereof and preferably is provided with at least one recess along its circumference. An elastic support surface preferably covers the circumference of each disk and is disposed between the disk and its outer plastic covering. The interior distance between the disks is from 20 to 69 mm. A circumferential recess preferably is disposed in at least on of the lateral surfaces of the plastic covering of each supporting disk. An electric motor drives a drive pulley, and the two are mounted in a stationary mounting while a swivellable pillow block moves the shaft to press against the drive pulley for driving the shaft and rotating the rotor. The center of gravity of the spinning rotor is at a distance of from 15 to 28 mm in front of the closest of the two pairs of supporting disks to the rotor. The free end of the rotor bears against an axial bearing and extends from 5 to 30 mm beyond the pair of supporting disks farthest away from the rotor and in the direction of the axial bearing.