Method for the documented tightening or retightening of a screw connection made up of a threaded bolt and a nut screwed on to the latter and supported on a flange surface, in which an exchangeable socket of a tensioning cylinder supported against the flange surface is screwed on to the free threaded end of the threaded bolt, the exchangeable socket is hydraulically tightened with longitudinal expansion of the threaded bolt and in the meantime the nut is corotated by rotation of a rotary sleeve connected to the nut for conjoint rotation, wherein switching means, in a first operating mode, allow only the exchangeable socket to be electrically driven and, in a second operating mode, allow only the rotary sleeve to be electrically driven, wherein, using a process control unit provided with a documentation module, a) the screw connection is identified by means of a sensing device arranged on the tensioning cylinder, and an identity feature characterizing the individual screw connection is stored in the documentation module, b) after the tensioning cylinder has been placed on the screw connection, a distance from the flange surface is sensed by means of a distance sensor arranged on the tensioning cylinder, and a corresponding first distance signal is transmitted to the process control unit, c) then, in the first operating mode, the exchangeable socket is screwed on to the free threaded end, and the distance from the flange surface is again sensed by means of the distance sensor, and a corresponding second distance signal is transmitted to the process control unit, d) the process control unit determines, from the difference between the distance signals (A1, A2), the size of the thread engagement between the exchangeable socket and the free threaded end of the threaded bolt, and the process control unit enables switching into the second operating mode only if there is a predefined minimum amount of thread engagement, e) after switching into the second operating mode, the threaded bolt is longitudinally expanded, and a load value that is characteristic for the tension force acting on the exchangeable socket and/or for the hydraulic pressure applied is stored in the documentation module and assigned to the respective identity feature, f) during the longitudinal expansion, the rotary sleeve is driven, and the drive torque and/or the angle of rotation covered by the rotary sleeve is stored in the documentation module and assigned to the respective identity feature. a) the screw connection is identified by means of a sensing device arranged on the tensioning cylinder, and an identity feature characterizing the individual screw connection is stored in the documentation module, b) after the tensioning cylinder has been placed on the screw connection, a distance from the flange surface is sensed by means of a distance sensor arranged on the tensioning cylinder, and a corresponding first distance signal is transmitted to the process control unit, c) then, in the first operating mode, the exchangeable socket is screwed on to the free threaded end, and the distance from the flange surface is again sensed by means of the distance sensor, and a corresponding second distance signal is transmitted to the process control unit, d) the process control unit determines, from the difference between the distance signals (A1, A2), the size of the thread engagement between the exchangeable socket and the free threaded end of the threaded bolt, and the process control unit enables switching into the second operating mode only if there is a predefined minimum amount of thread engagement, e) after switching into the second operating mode, the threaded bolt is longitudinally expanded, and a load value that is characteristic for the tension force acting on the exchangeable socket and/or for the hydraulic pressure applied is stored in the documentation module and assigned to the respective identity feature, f) during the longitudinal expansion, the rotary sleeve is driven, and the drive torque and/or the angle of rotation covered by the rotary sleeve is stored in the documentation module and assigned to the respective identity feature.