The gearbox comprises an engagement sleeve movable between a neutral position and one engagement position for engagement of one given gear, and a shift fork operatively connected to the engagement sleeve for controlling the movement thereof between the neutral position and the engagement position. The shift fork is slidably mounted on a stationary support rod, which is provided with a pair of bushes defining a first axial abutment surface for stopping the movement of the shift fork in the direction from the neutral position to the engagement position and a second axial abutment surface for stopping the movement of the shift fork in the direction from the engagement position to the neutral position. The neutral position of the shift fork is axially spaced from the second axial abutment surface.