A method for cyclically conveying sheets through a printing-technological machine adjusts a sheet position with high accuracy. The sheets following one another are in each case held at the front edge in grippers of a gripper system during the conveyance, and wherein the sheet position is adjusted in that a pneumatic apparatus is actuated by a control device which processes signals from at least one fixed-location sensor for the sheet position, as at least one sheet runs past, a large number of measured position values of the sheet are determined successively by using at least one sensor, from the measured position values a characteristic value for the sheet position being determined in the control device, the characteristic value as actual value being compared with a setpoint, and the pneumatic apparatus being set for a following sheet as a function of the comparison in each case between the actual and intended value of the preceding sheet.