A bent-axis hydrostatic axial piston machine (1) has a drive shaft (4) rotatable around an axis of rotation (R.sub.t) and having a drive flange (3). A cylinder drum (7) is rotatable around an axis of rotation (R.sub.z). The cylinder drum (7) includes a plurality of piston bores (8) concentric to the axis of rotation (R.sub.z) of the cylinder drum (7) and in each of which piston bores (8) there is a longitudinally displaceable piston (10). The pistons (10) are fastened in an articulated manner to the drive flange (3). Between the drive shaft (4) and the cylinder drum (7) there is a constant velocity driving joint (30) in the form of a cone-beam semi-roller joint (31).