Gear shift actuator comprising a linear drive assembly having a rotary member which is supported in a housing to be rotatable, but unmovable in an axial direction defined by its rotary axis, an electric motor for rotating the rotary member, and a driven component engaged by the rotary member to transmit rotary movement of the rotary member into a linear movement of the driven component along the axial direction for driving a shift fork from a neutral position to a first gear engaged position and back to neutral, when the rotary member is driven to rotate in a first sense of rotation and in a second sense of rotation opposite to the first sense of rotation, respectively, characterized in that the rotary member comprises a hollow cylindrical sleeve which is provided with a first cam follower projecting inwardly from an inner wall of the sleeve, the driven component comprises a first barrel cam which has a helical cam groove in its outer wall configured to receive the first cam follower and which is supported in the sleeve by a central rod to be slidably moveable in the sleeve along the central rod in axial direction but to be locked against rotational movements around the axial direction with respect to the central rod, the central rod is supported in the housing to be moveable in axial direction but to be locked against rotational movements around the axial direction, and carries a second end stop coupled thereto at a distance to the first barrel cam, the central rod being configured to project from the housing and to be linked to a shift fork for driving it, a compression mechanism is configured to extend the central rod from the first barrel cam by biasing the second end stop away from the first barrel cam, wherein the biased movement of the central rod is limited by a first end stop on the central rod abutting against the first barrel cam, and the helical cam groove is configured such that rotation of the sleeve in the first sense of rotation moves the first barrel cam axially in a first direction, which movement is transmitted via the compression mechanism to the central rod to drive a coupled shift fork from the neutral position towards the first gear engaged position, and such that rotation of the sleeve in the second sense of rotation moves the first barrel cam in an opposite second direction, which movement is transmitted to the central rod to drive a coupled shift fork from the first gear engaged position to the neutral position. the rotary member comprises a hollow cylindrical sleeve which is provided with a first cam follower projecting inwardly from an inner wall of the sleeve, the driven component comprises a first barrel cam which has a helical cam groove in its outer wall configured to receive the first cam follower and which is supported in the sleeve by a central rod to be slidably moveable in the sleeve along the central rod in axial direction but to be locked against rotational movements around the axial direction with respect to the central rod, the central rod is supported in the housing to be moveable in axial direction but to be locked against rotational movements around the axial direction, and carries a second end stop coupled thereto at a distance to the first barrel cam, the central rod being configured to project from the housing and to be linked to a shift fork for driving it, a compression mechanism is configured to extend the central rod from the first barrel cam by biasing the second end stop away from the first barrel cam, wherein the biased movement of the central rod is limited by a first end stop on the central rod abutting against the first barrel cam, and the helical cam groove is configured such that rotation of the sleeve in the first sense of rotation moves the first barrel cam axially in a first direction, which movement is transmitted via the compression mechanism to the central rod to drive a coupled shift fork from the neutral position towards the first gear engaged position, and such that rotation of the sleeve in the second sense of rotation moves the first barrel cam in an opposite second direction, which movement is transmitted to the central rod to drive a coupled shift fork from the first gear engaged position to the neutral position.