A turbomachine has a rotor shaft, which is mounted in a bearing arrangement containing a hydrodynamic axial bearing, and a rotor disposed on the rotor shaft. A hydrostatic axial bearing is additionally provided in the immediate vicinity of the hydrodynamic axial bearing, the hydrostatic axial bearing absorbing the axial force acting on the rotor shaft at rest, completely or at least for the most part, relieving stress on the hydrodynamic axial bearing during start-up processes of the rotor shaft, and being shut off during operation at the rated speed of rotation.