A worm gearbox having a worm wheel is arranged, in a torsionally resistant manner, on a steering shaft and rotates around a steering axis. A worm shaft is supported to rotate around a rotational axis, with the worm shaft having an end on the engine side and an end away from the engine. Worm toothing engages the teeth of the worm wheel and when the worm shaft rotates around the rotational axis, the worm wheel and the steering shaft rotate around the steering axis. A gearbox housing supports the worm wheel and the worm shaft and allows them to rotate. A compensating element has a middle section, a rear end section connected to the gearbox housing and a front end section retaining the end away from the engine of the worm shaft or a holder accommodating the end away from the engine of the worm shaft.