A hydrostatic axial piston machine (1) utilizing a bent-axis construction has a drive shaft (4) with a drive flange (3) rotatable around an axis of rotation (Rt) inside a housing (2). A cylinder barrel (7) is located inside the housing (2) and is rotatable around an axis of rotation (RZ). A drive joint (30) is located between the drive shaft (4) and the cylinder barrel (7). The drive joint (30) has at least one drive body (M1; M2; M3; M4) in the form of a slider or a roller body which is supported in the drive shaft (4) and the cylinder barrel (7). A lubrication device (80) is provided for the drive joint (30) and supplies lubricant from a lubricant port (81) located on the housing (2) of the axial piston machine (1) to the drive bodies (M1; M2; M3; M4) for cooling and lubrication of the drive bodies (M1; M2; M3; M4).