A transmission includes a first primary shaft carrying driving gearwheels for odd gears and reverse, a coaxial second primary shaft carrying driving gearwheels for the even gears, and a secondary shaft carrying idle driven gearwheels meshing with the driving gearwheels. The gearbox has a gear shift device having sliding engagement sleeves each arranged to connect a driven gearwheel corresponding to a given gear for rotation with a secondary shaft. Corresponding sliding shift forks cause an engagement sleeve to slide between a neutral and shift positions. A rotary drum has grooves on its cylindrical surface in which a stud slides, and is connected for translation with a respective shift fork in its sliding direction. An actuation unit rotates the drum stepwise among angular positions corresponding to engagement sleeves' predetermined positions. In a first angular position the engagement sleeves simultaneously engage gear reverse.