Abstract: The invention refers to an axial-piston pump or motor, having a piston which defines, with a cylinder, a chamber. A first end of the piston bears against a plate by means of a hydrostatic shoe having a cavity in the bearing face, a duct connecting the chamber to that cavity and being furnished with a constriction.The piston has a recess which is arranged in the cylindrical portion of its second end remote from the first end, the constriction being constituted by the clearance lying between at least one collar portion of the piston which separates the recess from the chamber and the cylinder. A second recess is provided in the piston, the constriction being located between the first and second recesses.The invention is applicable to the execution of a pump having high operational characteristics, particularly as far as concerns pressure.