Abstract: The device (10) comprises an electric motor (12), a reduction gear (14), a shaft (16) operable by the motor (12) via the reduction gear (14), and a drum (18) mounted on the shaft (16) so as to be connected for rotation therewith but free to slide axially relative thereto. The drum (18) has on its cylindrical lateral surface a first groove (20) in which first studs (22) drivingly connected for translation each with a respective shift fork (24) are guided, whereby the rotational movement of the drum (18) is converted into a translational movement of the studs (22), and hence of the forks (24), to bring about the engagement of the gears. The drum (18) also has a second groove (40) in which a second, axially stationary stud (42) engages.