Abstract: The axial piston machine, such as an engine or a pump, comprises a radial hydrostatic bearing for the drive shaft in the form of an oil gap between a conical shaft portion and a corresponding conical boring in a bearing block. The gap has a plurality of bearing pockets normally supplied with high-pressure oil via throttling means communicating with the high-pressure oil. An auxiliary axial hydrostatic bearing in the form of a bearing gap defined between the face of the bearing block near the tapering end of the bearing body and a radial extension of the drive shaft is supplied with an auxiliary low-pressure oil having an approximately constant pressure. A self-adjustable pressure chamber is provided in a plane parallel to the axial hydrostatic bearing gap and is defined by a collar supported on the drive shaft opposite the first radial extension and communicating with the axial bearing gap via a conduit.