The invention relates to a multiple-screw extruder that comprises a first process chamber (1) and a second process chamber (2). In the degassing zones of said extruder, at least the first process chamber is provided with at least one degassing opening. The radius R of the conveyor element in the degassing zones, in at least one conveyor element (7; 9) of at least one screw (5, 7; 5, 9) configured as a passage screw, in a subsection configured as a passage subsection (71a, 71e; 91a, 91e), along the peripheral direction of the at least one conveyor element (7; 9) is by ΔR smaller than the full radius Rv of the conveyor element (6; 8) required for the mutual stripping of adhering product in a closely intermeshing screw operation with die adjacent conveyor elements (6; 8) of adjacent conventional screws (5, 6; 5, 8). The invention also relates to a method for degassing viscous or elasticoviscous flowable masses in such a multi-screw extruder having several process chambers, the respective process chambers communicating by means of a connecting opening.