A hydrostatic axial piston machine (1), in particular an axial piston motor, has a rotating cylinder block (3) with a cylinder block body (3a) and a cylinder block neck (3b), and a drive shaft (14). Located in the cylinder block body (3a) are a plurality of piston bores (4) with pistons (5) that can move longitudinally and which are supported on a swashplate (7). Between the cylinder block neck (3b) which projects from the cylinder block body (3a) and extends in the direction of the swashplate (7) and the drive shaft (14) there is a synchronization gearing (20) and a braking device (25) that acts on the cylinder block (3). In the vicinity of the cylinder block neck (3b) within the axial dimension of the cylinder block body (3a), there is an additional synchronization gearing (21). The additional synchronization gearing (21) has a larger gear tooth clearance (SF) in the vicinity of the cylinder block body (3a) than the synchronization gearing (21) in the vicinity of the cylinder block neck (3b).