A twin wire press for dewatering solid-liquid suspensions, such as pulp suspensions, between top and bottom webs is described herein which includes consecutive primary, secondary and tertiary dewatering sections. The primary dewatering section includes a wedge area. The secondary dewatering section is positioned adjacent to the primary section downstream therefrom and includes grooved rolls in an s-roll configuration. The tertiary dewatering section includes rolls in a scissor-nip configuration. The press rolls in the secondary and tertiary section are all supported onto a frame. Whenever maintenance is to be performed on any one of the grooved rolls or on the press roll assemblies, an overhead crane can for example be used since no frame structure is provided on top thereof.