An apparatus and a method in connection with the lithography of structures on a micro or nanometer scale. A nano-imprinting apparatus according to an embodiment of the invention comprises two rotatably mounted rollers for transferring a pattern of micro or nanometer size to the substrate to be patterned. A first rotatably mounted roller has a patterned circumferential surface for transferring a pattern from the first rotatably mounted roller to a deformable substrate by contacting the patterned surface with the substrate. A second rotatably mounted roller has a principally smooth circumferential surface which faces the patterned surface of the first rotatably mounted roller. Furthermore, the second rotatably mounted roller is rotatably coupled with the first rotatably mounted roller for synchronized rotation of the first and second rollers. The substrate is movable between the first and second rollers such that, when these rollers rotate with respect to each other, the patterned surface of the first rotatably mounted roller comes into contact with the substrate whereby this pattern is transferred from the patterned surface to the substrate.