A hydrostatic axial piston machine includes a swashplate with an oblique surface formed thereon. Working pistons, which revolve and are supported by the oblique surface, are axially positioned on the swashplate with respect to a drive shaft. An adjusting cylinder, coupled to the swashplate, is configured to produce a pivoting moment and pivot the swashplate about a pivoting axis. Displacement of the working cylinders per revolution around the drive shaft is adjustable by adjusting a pivoting angle of the oblique surface. The adjustment of the pivoting angle is configured to pass beyond zero degrees, such that the direction of rotation of the drive shaft is changeable. The pivoting axis is at a distance from an axis of rotation of the drive shaft, such that an internal counter pivoting moment counteracting the pivoting moment is produced during operation of the axial piston machine when the working pistons are subjected to pressure.