A hydrostatic axial piston machine includes a drive shaft and a plurality of cylinder sleeves in which a spherical or ball-shaped section and a spherical or ball-shaped piston are inserted to delimit a respective displacer chamber. The sections are secured on a rotor, while the pistons are secured on a piston disk or piston drum. The piston disk is configured to be tilted at different pivoting angles relative to the rotor in a variable-displacement machine, or the piston disk is tilted continuously relative to the rotor in a constant-displacement machine. The rotor and the piston disk are coupled to one another for conjoint rotation by a driving device. The rotor and the piston disk can also be coupled indirectly by a drive shaft of the machine. A sliding joint axial with respect to a drive shaft is arranged between the rotor and the piston disk.