To provide a traverse-motion mechanism capable of easing the threading operation by reducing the heights of the yarn-separating fulcrum and the godet roller disposed upstream of a yarn-traversing fulcrum, of reducing times required for the manufacturing and assembling operation by simplifying the structure due to the reduction of the overall machine height, of minimizing the rise of selvage and ribbon wind generated in a package, and of readily adjusting the position of yarn turning point. A traversing unit 6-1 disposed at one end of the traverse-motion mechanism is offset from a regular position toward another traversing unit 6-4 so that a straight line connecting the opposite traverse ends (A) and (B) in the traversing unit 6-1 with each other is not parallel to an axis of a touch roller 7. In the traversing unit 6-1, three blades 15-1 through 15-3 are fixed on a first rotor 13 and two blades 20-1 and 20-2 are fixed on a second rotor 18 at equiangular positions in a rotary plane thereof, while the rotary centers of the first and second rotors 13, 18 are defined so that a rotary angle of the respective rotor, through which the yarn is conveyed by one blade on the one rotor while being in contact with the yarn-guiding surface 23 until released therefrom, is about 60.degree. in the first rotor 13 and 90.degree. in the second rotor 18 and a rotational ratio of the first rotor 13 relative to the second rotor 18 is 2:3.