Press section of a machine for producing a fiber material, web and process for guiding a fiber material web through the press section. The press section includes at least two double-felted presses arranged in series in a travel direction of the fiber material web. An upstream one of the at least two double-felted presses may include a deflection-controlled shoe press roll and a suction roll, and the deflection-controlled shoe press roll and the suction roll may be arranged to form an upstream press nip. The process may include guiding the fiber material web through a press nip of an upstream one of the at least two double-felted presses formed by a deflection-controlled shoe press roll and a suction roll.