A process for irradiating material in web form by means of electron beams and/or UV rays, wherein the material is applied to a transport means, the material on the transport means is guided through a first irradiation in which the material is irradiated in the open side, the material is transferred from the transport means to a substrate, and the material on the substrate is guided through a second irradiation in which the material is irradiated on the second, hitherto unirradiated, open side.