A strain wave reduction gear and a variable transmission ratio steering apparatus move a flexible gear (33) and a rigid gear (31) differentially, even if the flexible gear is in a fractured state. According to the strain wave reduction gear, the flexspline mates with the inner side of the elliptical hole of the rigid cam via the flexible bearing; therefore, the flexspline maintains an elliptical shape that is similar to the elliptical hole and maintains the meshed state-even if the flexspline fractures. Therefore, when the rigid cam rotates, the mesh positions of the flexspline and the first and second circular splines can be shifted in a circumferential direction. Namely, even in a state wherein the flexspline is fractured, the first circular spline and the second circular spline can be moved differentially by the difference in their tooth counts.
The tooth count of the external teeth (32A) is one or two fewer than that of the external teeth (31A). The tooth count of the internal teeth (33A) of the flexspline (33) is the same as that of the external teeth (32A).