A rotary printing press for printing a printing material, having: at least one printing unit comprising a forme cylinder for supporting a printing forme arrangement for displaying at least one print image on the printing material and for displaying at least two register marks, which are in an arrangement relationship with the print image, on the printing material adjacent to two opposite boundary edges of the printing material in an axial direction of the forme cylinder, at least one detection device, which is set up to automatically detect the register marks on the printing material at a scanning rate of once per rotation of the forme cylinder and to generate a detection signal for each detected register mark, wherein the detection device is further set up to detect a current machine acceleration of the rotary printing press at a scanning rate, which is increased as compared to the scanning rate of the register marks, a control device, which is connected to the detection device, which is set up to determine a circumferential register error of the print image on the printing material by comparing the detection signals for the register marks, which is set up to determine a current machine speed of the rotary printing press on the basis of the current machine acceleration, and which is set up to determine a compensation value for compensation of the circumferential register error on the basis of the circumferential register error in consideration of the current machine speed and to provide it as actuating signal, and an actuating device, which is connected to the control device and which is set up to automatically realize an offset based on the axial direction of the forme cylinder between the forme cylinder and the printing material by means of at least one actuating element (51, 52) on the basis of an actuating signal, so as to compensate the circumferential register error. at least one printing unit comprising a forme cylinder for supporting a printing forme arrangement for displaying at least one print image on the printing material and for displaying at least two register marks, which are in an arrangement relationship with the print image, on the printing material adjacent to two opposite boundary edges of the printing material in an axial direction of the forme cylinder, at least one detection device, which is set up to automatically detect the register marks on the printing material at a scanning rate of once per rotation of the forme cylinder and to generate a detection signal for each detected register mark, wherein the detection device is further set up to detect a current machine acceleration of the rotary printing press at a scanning rate, which is increased as compared to the scanning rate of the register marks, a control device, which is connected to the detection device, which is set up to determine a circumferential register error of the print image on the printing material by comparing the detection signals for the register marks, which is set up to determine a current machine speed of the rotary printing press on the basis of the current machine acceleration, and which is set up to determine a compensation value for compensation of the circumferential register error on the basis of the circumferential register error in consideration of the current machine speed and to provide it as actuating signal, and an actuating device, which is connected to the control device and which is set up to automatically realize an offset based on the axial direction of the forme cylinder between the forme cylinder and the printing material by means of at least one actuating element (51, 52) on the basis of an actuating signal, so as to compensate the circumferential register error.