A first endless felt belt (43) which absorbs water from the belt (9) passes through a first press nip (1) and a similar second felt belt (57) passes through a second press nip (II). The arrangement is such that the web (9) is continuously in contact with at least one transport means (for instance, with one of the felt belts). In both press nips (I, II) the web (9) is in contact with an endless elastic press element (for instance, press belt or press shell) the water absorption capacity of which is less than that of the felt belts (43, 57). It is essential that two endless elastic press elements which are independent of each other, namely a first and a second press element (47, 53) are present and that the one side of the web comes into contact with the first press element (47) in the first press nip (I) and the other side of the web comes into contact with the second press element (53) in the second press nip (II). The press section has neither a stone roll nor a suction press roll.