The control apparatus comprises, in its version intended for a double-clutch transmission, first, second and third shift forks each movable between first and second engagement positions to engage a respective gear, of which the first shift fork is able to engage at least the first gear and the second shift fork is able to engage at least the second gear, first, second and third double-acting hydraulic actuators arranged to control each the movement of a respective shift fork between the first and second engagement position, of which the first hydraulic actuator is associated to the first shift fork and the second hydraulic actuator is associated to the second shift fork, a slide valve selectively movable into one of at least three operating positions in each of which the slide valve selects a respective hydraulic actuator, and first and second gear shift solenoid valves for controlling the supply of fluid to the hydraulic actuator each time selected by the slide valve or the connection of that actuator to a tank. The first shift fork is moved into the engagement position of the first gear upon energization of the first gear shift solenoid valve, whereas the second shift fork is moved into the engagement position of the second gear upon energization of the second gear shift solenoid valve.