A cylinder apparatus of a sheet-fed rotary printing press having grippers (54) which are pivotally supported inside a notch in a blanket cylinder (20) brought into rolling contact with a plate cylinder (19) and which are located in the vicinity of the leading edge of the printing plate (21) wherein phases of rotation of the plate and blanket cylinders are adjusted such that the leading edge of the printing plate opposes a front end of the notch formed in the blanket cylinder which is located slightly at a downstream side of a leading edge of the blanket (51) and a cam surface of a cam (57) for opening closing the grippers has a shape in such a manner that the grippers are kept opened when the leading edge of the printing plate opposes the front end of the notch formed in the blanket cylinder.