A press section for a paper machine employing at least two press nips placed one after the other. Of these nips, at least the first nip is an extended nip or an extended roll nip. The last nip in the press section is placed on a level higher than the preceding nip. The first nip and/or, when more than two nips are employed, the nip that immediately precedes the last nip is/are provided with two press fabrics that receive water. The paper web is transferred on the lower fabric of the two press fabrics onto an upper fabric of the last nip. On the lower face of the upper fabric, the web is transferred into the last nip. After the web transfer point, the upper fabric of the last nip has a relatively short upwardly inclined run. After this, the upper fabric is turned and guided by the lower roll of the last nip over a considerable sector thereof. The last nip is placed after, or at the vicinity of, the uppermost point of the lower roll that forms the last nip. The point of transfer of the web onto the drying wire of the first group in the dryer section following after the press section is placed underneath the level of the last nip.