A multiple-shaft extruder comprises a core (4) with outward leading channels that can be flown through by a cooling liquid. At least two housing segments (16 to 19) are each provided with a cooling circuit with interconnected cooling bore holes (28), which can be flown through by a cooling liquid, are distributed in the peripheral direction and in an axially parallel manner, and which are located on the section of the housing segments (16 to 19) that faces the process chamber (2).