A hydraulic screw bolt tensioning device for tensioning screw bolts which pass through machine parts (90, 91) to be clamped to each other and include a bolt head, which is supported on one side of the machine parts, and have a bolt end which is provided for being screwed to the screw bolt tensioning device, wherein the bolt end includes an external thread and at least one internal thread extending from the end face along the bolt axis, comprising - a cylinder with a cylinder axis, which on a first end face includes a supporting surface for supporting on the machine parts, - an outer exchange bushing which is arranged in the cylinder so as to be axially shiftable relative to the same and includes a first portion with an internal thread for screwing onto the external thread of the bolt end and a second portion with an axial through bore which opens into the first portion, - an inner exchange bushing which passes through the cylinder and the through bore of the outer exchange bushing and is rotatable and axially shiftable relative to the same and at a first end includes an external thread which can be screwed to the internal thread of the bolt end, - a first piston which is firmly connected to the outer exchange bushing and is axially shiftable in the cylinder by a pressure medium in the direction facing away from the supporting surface, wherein the cylinder includes a first pressure medium supply, - a second piston which is firmly connected to the inner exchange bushing and is axially shiftable in the cylinder by a pressure medium in the direction facing away from the supporting surface, wherein the cylinder includes a second pressure medium supply, - wherein the size ratio of the effective piston surfaces of the first and second pistons (12, 7) relative to each other corresponds to the size ratio between the components of the total pretensioning force to be transmitted by the outer and inner exchange bushings (11, 2), - a pressure medium port which is in flow connection with the first and with the second pressure medium supply. - a cylinder with a cylinder axis, which on a first end face includes a supporting surface for supporting on the machine parts, - an outer exchange bushing which is arranged in the cylinder so as to be axially shiftable relative to the same and includes a first portion with an internal thread for screwing onto the external thread of the bolt end and a second portion with an axial through bore which opens into the first portion, - an inner exchange bushing which passes through the cylinder and the through bore of the outer exchange bushing and is rotatable and axially shiftable relative to the same and at a first end includes an external thread which can be screwed to the internal thread of the bolt end, - a first piston which is firmly connected to the outer exchange bushing and is axially shiftable in the cylinder by a pressure medium in the direction facing away from the supporting surface, wherein the cylinder includes a first pressure medium supply, - a second piston which is firmly connected to the inner exchange bushing and is axially shiftable in the cylinder by a pressure medium in the direction facing away from the supporting surface, wherein the cylinder includes a second pressure medium supply, - wherein the size ratio of the effective piston surfaces of the first and second pistons (12, 7) relative to each other corresponds to the size ratio between the components of the total pretensioning force to be transmitted by the outer and inner exchange bushings (11, 2), - a pressure medium port which is in flow connection with the first and with the second pressure medium supply.