Abstract: During the production of a preform of thermoplastic synthetic material by means of extrusion from an extruder head provided with a slot-shaped exit opening, the width of which is changed according to a specific program during the extrusion of the preform in order to change the wall thickness thereof, the wall thickness of at least one section of the preform should be controlled by at least one additional program, which is superposed on at least one portion of the first program, which is longer than the additional program. In this manner, one achieves greater flexibility in respect to fulfilling the requirements of each situation on the programming, namely both in respect to the resolution and in respect to precise determination of the location of the individual switch points, even when a very great number of changes of the slot width must be undertaken over a very short section of the preform or during a very short time period during the extrusion process.