A gearbox actuator comprising: an electric motor, a shaft member rotatable about a gearbox axis, and adapted for its mechanical connection with a gearbox shaft of a motor vehicle, a transmission mechanism coupled with the electric motor and couplable with the shaft member for transmitting a rotation movement from the electric motor to the shaft member to bring the shaft member to selected angular positions for shifting gears, and wherein the gearbox actuator is configured such that the transmission mechanism can move in a direction in which it is coupled in one rotation direction with the shaft member to rotate the shaft member towards a gearbox position, characterized in that: the gearbox actuator further comprises an electronic controller electrically connected to the electric motor to operate the same, wherein the electronic controller is adapted such that the transmission mechanism uncouples from the shaft member, so the shaft member can rotate freely to reach a stable gear position, and wherein the electronic controller is further adapted to reverse rotation direction of the electric motor shaft for a determined angular displacement, in order to reverse movement of the transmission mechanism and uncouple the same from the shaft member, so the shaft member can rotate freely to reach a stable gear position in both directions, and wherein the gearbox actuator is configured such that the transmission mechanism reverses movement direction and uncouples from the shaft member so as to create a separation gap between the shaft member and the transmission mechanism, that allows the shaft member to rotate freely to reach a stable gearbox position. an electric motor, a shaft member rotatable about a gearbox axis, and adapted for its mechanical connection with a gearbox shaft of a motor vehicle, a transmission mechanism coupled with the electric motor and couplable with the shaft member for transmitting a rotation movement from the electric motor to the shaft member to bring the shaft member to selected angular positions for shifting gears, and wherein the gearbox actuator is configured such that the transmission mechanism can move in a direction in which it is coupled in one rotation direction with the shaft member to rotate the shaft member towards a gearbox position, characterized in that: the gearbox actuator further comprises an electronic controller electrically connected to the electric motor to operate the same, wherein the electronic controller is adapted such that the transmission mechanism uncouples from the shaft member, so the shaft member can rotate freely to reach a stable gear position, and wherein the electronic controller is further adapted to reverse rotation direction of the electric motor shaft for a determined angular displacement, in order to reverse movement of the transmission mechanism and uncouple the same from the shaft member, so the shaft member can rotate freely to reach a stable gear position in both directions, and wherein the gearbox actuator is configured such that the transmission mechanism reverses movement direction and uncouples from the shaft member so as to create a separation gap between the shaft member and the transmission mechanism, that allows the shaft member to rotate freely to reach a stable gearbox position. the gearbox actuator further comprises an electronic controller electrically connected to the electric motor to operate the same, wherein the electronic controller is adapted such that the transmission mechanism uncouples from the shaft member, so the shaft member can rotate freely to reach a stable gear position, and wherein the electronic controller is further adapted to reverse rotation direction of the electric motor shaft for a determined angular displacement, in order to reverse movement of the transmission mechanism and uncouple the same from the shaft member, so the shaft member can rotate freely to reach a stable gear position in both directions, and wherein the gearbox actuator is configured such that the transmission mechanism reverses movement direction and uncouples from the shaft member so as to create a separation gap between the shaft member and the transmission mechanism, that allows the shaft member to rotate freely to reach a stable gearbox position.