An electric power steering system with a worm gear includes a worm shaft and a worm wheel, wherein an electric motor is associated with the worm shaft, which is connected to the worm shaft in a force-transmitting manner. A bearing element, arranged on the worm shaft at the end of the worm shaft facing away from the electric motor, is received in a guide bush, wherein the guide bush has, on its circumferential side, a passage opening. It is provided a pre-tensioning device comprising a spring-loaded actuator element extending through the passage opening of the guide bush and acting on the worm shaft in the direction of the worm wheel with a defined pre-tensioning force (K), wherein the pre-tensioning device comprises a limiting device which is adapted to limit a pivoting movement that displaces the worm wheel away from the worm shaft. Furthermore, it is proposed a method for the production of steering systems and a test system for performing the method.