The dryer section of a machine for manufacturing a paper web includes at least one and more usually a plurality of heatable drying cylinders, each of which is wrapped over a part of its circumferential surface by the web of material to be dried. A support belt is guided by guide rolls to wrap over a part of the circumference of each of the drying cylinders and over the web. A pressing device presses against the support belt to press the web of material against the drying cylinder. That pressing device may comprise a pressure box outside the support belt to which air or steam pressure is applied. The pressure box may include several zones either along the web path or transverse to the web path permitting different pressures to be applied. The pressing device may alternately comprise a plurality of pressing rolls extending transversely to the web axis and parallel to the drying cylinder axis and being biased against the support belt, e.g., by springs, and supported on a support which moves the pressing rolls toward the support belt.