To simply mount an outer ring of bearing supporting a speed-reduction rotation output element of a wave gear transmission in the rotating state a cylindrical housing with no deformation.

In the wave gear device unit 1, a wave gear transmission 3 is disposed in a cylindrical housing 2 and a cup-shaped flexible external tooth gear 6, i.e., an output element, is supported in the housing 2 through a cross roller bearing 4. An outer ring 11 of the cross roller bearing 4 is threadly fixed to the housing 2. In the case where the outer ring is tightened using a plurality of tightening bolts, a deformation of the outer ring and an unbalance of a circumferential axial tension distribution can be inhibited. Since the number of assembling steps can be reduced and the number of processing steps such as a boring and a tap processing can be reduced, a manufacture cost can be reduced. Since a tightening bolt is not required, the unit can be made to a small size and a compact size.