A sequential control device having a rotatable drum and having a plurality of guide grooves and a corresponding plurality of engagement forks, each including a supporting portion on the outer surface of the drum, a drive portion to drive a corresponding synchronizing sleeve of the gearbox, and a pin engaging in a corresponding guide groove of the drum. The guide grooves are shaped to produce selective axial movement of the pins and engagement forks, upon rotation of the drum, to cause each time the engagement of a given gear. The pins are positioned on the same side of the drive portion of the engagement forks. A through groove is provided on the outer surface of the drum and extends from an end of the drum to at least the guide groove farthest from that end, to guide the pins of the engagement forks when mounted on the drum.