A sheet gripping arrangement of a rotary printing machine has a sheet gripper abutment member, a soft gripper seat member, a gripper shaft having a gripper shaft pivot point, a sheet gripping element including a gripper finger cooperating with the gripper seat member and eccentrically pivotable relative to the gripper shaft about a gripper finger pivot point so as to move first over a substantially flat gripping path and then to move during its final movement phase normally to the latter, and a threaded abutment member arranged in the finger member and acting against the sheet gripper abutment member, wherein the gripper finger member is arranged at an angle of substantially 90.degree. to a contact point of the threaded abutment member with the sheet gripper abutment member, to the gripper finger point, and to the gripper shaft pivot point.