The press section of a papermaking machine for dewatering a paper web comprises two separate, successively arranged extended nip press locations. Both of the extended nip press locations contain at least one respective felt which travels together with the paper web through the associated extended nip press location. The paper web is guided from the first extended nip press location to a web removal device contacted by an upper felt of the second extended nip press location, and from that location the paper web can move to the second extended nip press location.