Abstract: Continuous motion apparatus having an offset blanket wheel for applying main images to cylindrical containers is also provided with a plurality of direct printing units that apply auxiliary images to the containers. All of the cassettes are mounted on the blanket wheel. Each cassette is provided with at least one belt having a plurality of auxiliary images in tandem. The belt or belts, as the case may be, is driven continuously at uniform speed along a closed loop path. The cylindrical outer surface having images applied thereto travels at the same linear speed as the offset blanket, and there is a difference in linear speeds between the belt with the auxiliary images thereon and the cylindrical outer surface, even while the auxiliary images are being applied to the cylindrical outer surface.