A process for drawing stretched metal workpieces, especially tubes, for the purpose of cross-sectional reduction in more than one drawing step using at least two sequential drawing aggregates. The aggregates grip the workpiece on the outer periphery, with two alternately-moved clamping carriages, which draw the workpiece continuously through respective drawing rings associated with the respective aggregates and arranged in respective drawing-ring holders. The drawing aggregates can be driven independently of one another in a power-regulated and/or moment-regulated manner. Furthermore, during the drawing process, a defined prestress force, which prevents deflection of the workpieces from a straight line, is maintained at all times in the section of the workpiece located between the drawing aggregates.