A viscoelastic material is extruded by kneading-and-conveying screws of different respective diameters positioned coaxially and telescopingly. A flight trough of a larger-diameter screw has radial orifices allowing a first space swept by the flight of the larger-diameter screw to communicate with a second space swept by a flight of a smaller-diameter screw. A fixed cylindrical tube arranged coaxially with the screws is disposed radially between the first and second spaces within the region in which the screws telescope. The tube has radial apertures therethrough to conduct material from the orifices to the second space. The first space is closed off at an axial end thereof by a wall where foreign substances accumulate that do not pass through the orifices. A passage through the wall can be opened to remove the accumulated substances without interrupting the extrusion operation.