A multi-stage transmission wherein a drive gear shaft and a driven gear shaft are disposed in parallel; a group of drive gears (m) and a group of driven gears (n) are supported on the drive gear shaft and the driven gear shaft, respectively, in a manner that the drive gears (m) and the driven gears (n) are constantly meshed with each other to constitute meshing gear combinations for different speeds corresponding to different reduction gear ratios; one group (m) of the group of the drive gears (m) and the group of the driven gears (n) being fixed to the gear shaft supporting the one group (m), while the gear shaft supporting the other group (n) of the group of the drive gears (m) and the group of the driven gears (n) is a hollow gear shaft; and the gears of the other group of gears (n) are supported on the hollow gear shaft individually in an engageable and disengageable manner through engaging means, which are operated by gear shift driving means for gear shift, characterized in that: said engaging means comprises: engaging parts provided on an inner peripheral surface of each of the gears of the other group of gears (n) at circumferentially spaced positions and having engaging surfaces in circumferential directions; a first engaging device provided in the hollow gear shaft to cause the engaging parts of a first gear of the gears of the other group of gears (n) and the hollow gear shaft to be engaged with each other only in a rotational direction of the gears of the other group of gears (n); a second engaging device provided in the hollow gear shaft to cause the engaging parts of a second gear, one step lower in reduction gear ratio than the first gear, of the other group of gears (n) and the hollow gear shaft to be engaged with each other only in the rotational direction of the gears of the other group of gears (n); a third engaging device provided in the hollow gear shaft to cause the engaging parts of the first gear and the hollow gear shaft to be engaged with each other only in a counter-rotational direction of the gears of the other group of gears (n); a fourth engaging device provided in the hollow gear shaft to cause the engaging parts of the second gear and the hollow gear shaft to be engaged with each other only in the counter-rotational direction of the gears of the other group of gears (n); first cam rods put in sliding contact with an inner peripheral surface of an internal hole of the hollow gear shaft so as to be movable in an axial direction, and provided in sliding contact surfaces thereof with a plurality of cam surfaces at axially spaced locations to operate the second engaging device and the third engaging device by movement thereof; and second cam rods put in sliding contact with the inner peripheral surface of the internal hole of the hollow gear shaft so as to be movable in the axial direction, and provided in sliding contact surfaces thereof with a plurality of cam surfaces at axially spaced locations to operate the first engaging device and the fourth engaging device by movement thereof; the first cam rods and the second cam rods being moved by the gear shift driving means so as to make a gear shift. engaging parts provided on an inner peripheral surface of each of the gears of the other group of gears (n) at circumferentially spaced positions and having engaging surfaces in circumferential directions; a first engaging device provided in the hollow gear shaft to cause the engaging parts of a first gear of the gears of the other group of gears (n) and the hollow gear shaft to be engaged with each other only in a rotational direction of the gears of the other group of gears (n); a second engaging device provided in the hollow gear shaft to cause the engaging parts of a second gear, one step lower in reduction gear ratio than the first gear, of the other group of gears (n) and the hollow gear shaft to be engaged with each other only in the rotational direction of the gears of the other group of gears (n); a third engaging device provided in the hollow gear shaft to cause the engaging parts of the first gear and the hollow gear shaft to be engaged with each other only in a counter-rotational direction of the gears of the other group of gears (n); a fourth engaging device provided in the hollow gear shaft to cause the engaging parts of the second gear and the hollow gear shaft to be engaged with each other only in the counter-rotational direction of the gears of the other group of gears (n); first cam rods put in sliding contact with an inner peripheral surface of an internal hole of the hollow gear shaft so as to be movable in an axial direction, and provided in sliding contact surfaces thereof with a plurality of cam surfaces at axially spaced locations to operate the second engaging device and the third engaging device by movement thereof; and second cam rods put in sliding contact with the inner peripheral surface of the internal hole of the hollow gear shaft so as to be movable in the axial direction, and provided in sliding contact surfaces thereof with a plurality of cam surfaces at axially spaced locations to operate the first engaging device and the fourth engaging device by movement thereof; the first cam rods and the second cam rods being moved by the gear shift driving means so as to make a gear shift.