A dual clutch transmission unit (1) for a motor vehicle (3) is adapted to transmit the movement to an automatic gear change (5) provided with two ranks of gears; the transmission unit (1) has a rotary movement input member (45) adapted to be driven in rotation by the engine (4) of the motor vehicle (3) and two output shafts (29, 30) which are adapted to be rigidly connected to respective input shafts (9, 10) of the gear change (5) and bear respective clutch devices (39, 40) which are adapted to receive the movement from the rotary member (45) and are each associated with a relative rank of gears of the gear change (5); one of the clutch devices (39, 40) is disengaged and the other is engaged in sequence by an actuator device (15) provided with a single actuator (70) and a movement sleeve (81) coaxial with one another.