A multiple-stage positioning structure of dual shafts includes a dual shaft assembly, which includes first and second rotary shafts that are connected to each other with coupling members for being rotated synchronously. The first rotary shaft has a curved section and a planar section. Positioning sleeves are fit over the first and the second rotary shafts. Bearing members bear a positioning bar in such a way to have the planar section of the first rotary shaft in contact engagement with a lateral planar section of the positioning bar. When the first rotary shaft is rotated to have the curved section engage the lateral planar section of the positioning bar, an effect of outward expanding and stretching the positioning sleeves is induced. When the first rotary shaft is rotated to have the planar section re-engage the lateral planar section of the positioning bar, an effect of positioning is induced.
