A wave gear unit has an input shaft positioned along a center axis by first and second input bearings. A first unit end plate at the first-input-bearing side is a composite member in which a bearing housing member of an iron-based material is integrated with an end plate main body member of a lightweight material. A second unit end plate at the second-input-bearing side is integrated with a rigid internally toothed gear, and is a composite member in which a second member of a lightweight material is integrated with a first member of a lightweight material. The first member has an end plate main body portion of the second unit end plate and a gear main body portion of the rigid internally toothed gear, while the second member has a bearing housing portion of the second unit end plate and a teeth formation portion of the rigid internally toothed gear.