The extruder screw drive has a first and a second motor, a screw mechanism connected to the first motor and to the extruder screw for translating it in the extrusion cylinder, and a slide mechanism connected to the second motor and to the extruder screw for rotating it in the extrusion cylinder. The screw mechanism and the slide mechanism are coaxial and partially fit into one another to provide an axially compact arrangement. The motors can be hollow shaft electric motors axially aligned together, and pressure regulated hydraulic axial force can be added to the extruder screw during plasticating as it retracts due to increased volume of plastic at an output end of the extrusion cylinder.