A hydraulic axial piston pump having a floating rotatory drum, comprising: - a housing provided with: a first inlet for the intake of a primary liquid; a first outlet for the delivery of said primary liquid at a high pressure; a second inlet for the intake of a secondary liquid at a pressure that is lower than the delivery pressure of the primary liquid and a second outlet for the delivery of said secondary liquid; - a drum provided with a drive shaft and with a plurality of cylinders arranged in circular fashion around the geometric axis of said drum and communicated at its ends with first inlet and outlet mouths of the primary liquid and with second inlet and outlet mouths of the secondary liquid, said first and second mouths (23, 24) being defined at a first end and at a second end of the drum; - pistons mounted in the respective cylinders and being prolonged in rods projecting through one end of the drum and ending in supporting shoes on a fixed inclined plate; - a first fluid-distributing plate and a second fluid-distributing plate, facing opposite ends of the drum and provided with openings (51, 52) suitably distributed for establishing in an alternating manner, during rotation of the drum, the connection between first mouths of the cylinders and the first inlet and first outlet of primary liquid of the housing, and the connection between second mouths of the cylinders and the second inlet and second outlet of the secondary liquid, said connections being established such that it is synchronized with the direction of movement of the pistons inside the cylinders; characterized in that: first and second strips (6a, 6b) rotating together with the drum are mounted with certain clearance in the axial direction between a first end of the rotatory drum and the first distributing plate, and between a second end of the drum and the second distributing plate; said first and second strips (6a, 6b) having openings facing the first and second mouths (23, 24) of the drum and coupling means suitable for allowing a movement of the first and second strips (6a, 6b) in the axial direction with respect to the drum and the head-on actuation of said strips (6a, 6b) against the respective distributing plates (5a, 5b), said strips (6a, 6b) forming a sealed closure between the ends of the drum and the respective distributing plates (5a, 5b). - a housing provided with: a first inlet for the intake of a primary liquid; a first outlet for the delivery of said primary liquid at a high pressure; a second inlet for the intake of a secondary liquid at a pressure that is lower than the delivery pressure of the primary liquid and a second outlet for the delivery of said secondary liquid; - a drum provided with a drive shaft and with a plurality of cylinders arranged in circular fashion around the geometric axis of said drum and communicated at its ends with first inlet and outlet mouths of the primary liquid and with second inlet and outlet mouths of the secondary liquid, said first and second mouths (23, 24) being defined at a first end and at a second end of the drum; - pistons mounted in the respective cylinders and being prolonged in rods projecting through one end of the drum and ending in supporting shoes on a fixed inclined plate; - a first fluid-distributing plate and a second fluid-distributing plate, facing opposite ends of the drum and provided with openings (51, 52) suitably distributed for establishing in an alternating manner, during rotation of the drum, the connection between first mouths of the cylinders and the first inlet and first outlet of primary liquid of the housing, and the connection between second mouths of the cylinders and the second inlet and second outlet of the secondary liquid, said connections being established such that it is synchronized with the direction of movement of the pistons inside the cylinders;