Abstract: An apparatus for drying and smoothing a fibre web (5) between two tight bands (1, 2) that move in parallel and turn around turning rolls (6a, 6b, 7a, 7b), the first band (1) being heated with hot steam and the second band (2) being cooled with water, and the fibre web (5) being conducted through the drying zone that the bands (1, 2) define together with at least one felt or wire (3, 4) such that the fibre web (5) is in contact with the surface of the first, heated band (1) and that the felt or wire (3, 4) is between the fibre web (5) and the second, cooled band (2). In the invention, the fibre web (5) is smoothed such that the press means located in the vicinity of the first turning rolls (6a, 7a) in the travel direction of the fibre web (5) apply to it a pressure that is essentially higher than the pressure in the other parts of the drying zone.