A hydrostatic positive displacement machine has an adjustable swept volume, and has a lifting element, a rotor with positive displacement elements supported on the lifting element, and a hydraulic adjusting device that adjusts the swept volume and includes an adjusting piston that is mounted in or on a cylinder, is movable axially rectilinearly in relation to the cylinder, and is adjacent to a pressurizable adjusting chamber. A bearing gap is formed between a circular-cylindrical bearing surface of the adjusting piston and a circular-cylindrical bearing surface of the cylinder. The adjusting piston is mounted hydrostatically, wherein at least three pressure pockets are distributed uniformly in a row over the circumference of a bearing surface. Pressure fluid flows into each pressure pocket via a fixed throttle, which is assigned only to the respective pressure pocket, and flows out of each pressure pocket via the bearing gap.