A press section in a paper machine through which a paper web has a closed and supported draw and a method and arrangement for compensating for elongation of the web in an equalizing press nip in the press section. The press section has at least two successive separate nips and dewatering of the paper web is carried out at least in the first one of these nips, preferably between two press fabrics that receive water. The last press nip in a running direction of the web is the equalizing press nip which may be separate from the preceding nip and in which no substantial dewatering is performed. The web may be passed through the equalizing press nip from the preceding dewatering press nip on a transfer belt substantially non-water-receiving. After the equalizing nip, the elongation of the paper web in the machine direction, which elongation takes place in the equalizing nip, is compensated for by a difference in speed of the transfer belt.