Abstract: The gearbox has synchronizers and at least one speed ratio set of gears which is non-synchronized. The synchronized set of gears are actuated by parallel longitudinally movable rods. A first rod which moves the movable means is connected to a second rod which relates to one of the synchronizers by automatically withdrawable connecting means so that the beginning of the displacement from its position of rest of the first rod causes a displacement of the second rod, said displacement, which precedes the engagement of the non-synchronized set of gears, being of such extent that it just puts the synchronizers into action without engaging the corresponding speed ratio. The second rod carries a slidable sleeve having withdrawable means for connection to the second rod and means for positively driving the second rod at the same time as the first rod.