A straightening press unit for a straightening press for trenchless pipeline construction, comprising: - At least one, preferably 2 to 4, double-acting cylinders comprising an inner pipe, a piston rod with piston, wherein the piston rod with the piston is inserted into the inner pipe, and the cylinder has a respective longitudinal or transverse borehole in the area of the cylinder ends, - A fixing block for receiving and fixing the at least one cylinder, - A pressing rod holder for fixing pressing rods and transferring force from the straightening press unit to the pressing rods, - A yoke, wherein the yoke connects the piston rod of the at least one cylinder with the pressing rod holder, as a result of which the movement of the piston rod performed by the cylinder is transferred to the pressing rod holder, and hence to the pressing rods fixed thereto, - At least a first and a second hydraulic oil line, wherein the hydraulic oil lines (61, 62) are connected with the longitudinal or transverse boreholes at the cylinder ends, wherein the at least one cylinder is arranged between the fixing block and the yoke, characterized in that i) the inner pipe of the cylinder is jacketed with a fiber-reinforced composite material, ii) the hydraulic oil line connected with the longitudinal or transverse borehole of the cylinder end arranged on the side of the cylinder facing away from the fixing block forms a first hydraulic oil line, wherein the latter is present in the form of a high-pressure hose or a high-pressure steel pipe, wherein the high-pressure steel pipe has a bend of at least 30°, in particular at least 45°, and/or is provided with at least one pluggable connection, and iii) the fixing block comprises at least one borehole for receiving a cylinder end of the at least one cylinder, an opening for passing through the pressing rods, a first and a second oil inlet/outlet for connection with an external hydraulic aggregate, an opening for receiving the first hydraulic oil line, the second, and a third hydraulic line, which are integrated in the fixing block, and possibly also at least one safety valve. - At least one, preferably 2 to 4, double-acting cylinders comprising an inner pipe, a piston rod with piston, wherein the piston rod with the piston is inserted into the inner pipe, and the cylinder has a respective longitudinal or transverse borehole in the area of the cylinder ends, - A fixing block for receiving and fixing the at least one cylinder, - A pressing rod holder for fixing pressing rods and transferring force from the straightening press unit to the pressing rods, - A yoke, wherein the yoke connects the piston rod of the at least one cylinder with the pressing rod holder, as a result of which the movement of the piston rod performed by the cylinder is transferred to the pressing rod holder, and hence to the pressing rods fixed thereto, - At least a first and a second hydraulic oil line, wherein the hydraulic oil lines (61, 62) are connected with the longitudinal or transverse boreholes at the cylinder ends, i) the inner pipe of the cylinder is jacketed with a fiber-reinforced composite material, ii) the hydraulic oil line connected with the longitudinal or transverse borehole of the cylinder end arranged on the side of the cylinder facing away from the fixing block forms a first hydraulic oil line, wherein the latter is present in the form of a high-pressure hose or a high-pressure steel pipe, wherein the high-pressure steel pipe has a bend of at least 30°, in particular at least 45°, and/or is provided with at least one pluggable connection, and iii) the fixing block comprises at least one borehole for receiving a cylinder end of the at least one cylinder, an opening for passing through the pressing rods, a first and a second oil inlet/outlet for connection with an external hydraulic aggregate, an opening for receiving the first hydraulic oil line, the second, and a third hydraulic line, which are integrated in the fixing block, and possibly also at least one safety valve.