Abstract: The invention has as its object the provision of a method and an apparatus for the generation of smoothness and gloss on paper which essentially precludes a re-erection of the surface fibers after the smoothing process. This is achieved in that the surface of a paper web (1) to be smoothed is heated to a temperature above the glass transition temperature of the fibers at the surface of the web without subjecting the web to a press nip, and then these fibers are deformed and fixed in the deformed state in a subsequent process step under the simultaneous action of pressure with shock cooling. Accordingly, there is associated with each surface of the paper web (1) to be smoothed a heating device (2) and also a subsequent cooled body (5, 9, 10) which presses against the surface.