Method for tightening screw connections which are situated at screw positions that are disposed in a row along two annular flanges that are to be tensioned in relation to one another, wherein each screw connection is composed of a threaded element and a nut screw-fitted thereon, and the nut is supported in relation to the one of the two annular flanges and the threaded element is supported in relation to the other of the two annular flanges , having a tool carrier which is capable of travelling along the ring that is formed by the annular flanges , the component parts of said tool carrier being at least one tool for tightening the screw connection and a sensor , characterized in that a) the tool carrier is moved along the entire length of the ring at least once, and in that repeatedly - the respective current longitudinal position of the tool carrier in relation to the ring is herein detected as a position value by means of a distance sensor disposed on the tool carrier , and - the size of the gap present between the two annular flanges at the respective current position is detected as the gap size value by means of the sensor , and these are transmitted to a control and evaluation unit which stores the individual gap size values conjointly with the respectively assigned position values as datasets; b) the control and evaluation unit from the gap size values contained in the datasets determines the largest gap size value or a gap size value of above-average size, and determines the position value assigned to said determined gap size value as a primary position; c) and the screw connection subsequently tightened by the tool is that screw connection that is situated at the primary position or at a screw position that in a circumferential direction directly follows the primary position. a) the tool carrier is moved along the entire length of the ring at least once, and in that repeatedly - the respective current longitudinal position of the tool carrier in relation to the ring is herein detected as a position value by means of a distance sensor disposed on the tool carrier , and - the size of the gap present between the two annular flanges at the respective current position is detected as the gap size value by means of the sensor , and these are transmitted to a control and evaluation unit which stores the individual gap size values conjointly with the respectively assigned position values as datasets; - the respective current longitudinal position of the tool carrier in relation to the ring is herein detected as a position value by means of a distance sensor disposed on the tool carrier , and - the size of the gap present between the two annular flanges at the respective current position is detected as the gap size value by means of the sensor , b) the control and evaluation unit from the gap size values contained in the datasets determines the largest gap size value or a gap size value of above-average size, and determines the position value assigned to said determined gap size value as a primary position; c) and the screw connection subsequently tightened by the tool is that screw connection that is situated at the primary position or at a screw position that in a circumferential direction directly follows the primary position. <EOS>