The invention relates to a fluid dynamic bearing system that has a stationary sleeve, a stationary shaft disposed in the sleeve and bearing disks disposed on the sleeve and shaft which form an annular disk-shaped space between each other in which an annular disk-shaped component is disposed. A bearing gap filled with a bearing fluid is formed between the stationary and the rotating bearing construction. The bearing system further comprises at least one radial bearing formed between the outer circumference of the shaft and the inner circumference of the annular disk-shaped component, at least two axial bearings formed by the two end faces of the annular disk-shaped component and the first end faces of the bearing disks opposing these; and capillary seals to seal the two open ends of the bearing gap, at least one capillary seal comprising a reservoir that is at least partly filled with bearing fluid and is formed between the surfaces opposing each other of the rotor hub, or a component connected to the rotor hub, and an end face of one of the bearing disks.