A transmission includes a first primary shaft carrying driving gearwheels associated to the odd gears and to the reverse gear, a second primary shaft coaxial to the first shaft and carrying driving gearwheels associated to the even gears, and at least one secondary shaft carrying a plurality of idle driven gearwheels directly or indirectly meshing with the driving gearwheels. The gearbox is also provided with a gear shift device having sliding engagement sleeves are each arranged to connect each time a driven gearwheel corresponding to a given gear for rotation with the respective secondary shaft. Corresponding sliding shift forks are each arranged to cause a respective engagement sleeve to slide between a neutral position and at least one shift position. A rotary drum has a corresponding guide grooves on its outer cylindrical surface in each of which a respective stud slidably engages, and is rigidly connected for translation with a respective shift fork in the sliding direction of the shift fork. An actuation unit is arranged to cause the drum to rotate stepwise among angular positions, each corresponding to predetermined positions of the engagement sleeves. The guide grooves of the drum are shaped so that in a first angular position the engagement sleeves are positioned to engage at the same time the second gear and the reverse gear.