For the production of embossed microstructures in radiation-curing materials, use is made of a micro embossing form fixed to a reflective or scattering cylinder surface. Via a press nip, the micro embossing form comes into contact with the substrate guided over a cylinder or a deflection roller. The radiation-curing material is acted on in one or both pockets, before or after the press nip, with radiation which penetrates into the press nip by reflection or scattering.