To provide an engagement member and a wave gear which are resistant to the occurrence of eccentricity and inclination of a sleeve and an inner shaft at the time of insertion, and which are resistant to the occurrence of displacements of an axial center caused by the opening of the sleeve or the like.

The engagement member is provided with the nearly cup-shaped sleeve 6 and the cylindrical inner shaft 7. At least either the sleeve 6 or the inner shaft 7 is made of a shape-memory alloy. The inner diameter surface of the sleeve 6 is provided with a tapered groove 8, which expanded to the opening end side. Then the inner shaft 7, which is engaged with the groove 8, has a convexity which is engaged with the groove 8. In order to gain a fastening force between the sleeve 6 and the inner shaft 7, the sleeve 6 is made so that its inner diameter is smaller than the outer diameter of the inner shaft 7.

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