A wave generator (4) of a wave gear device (1) bends an externally toothed gear (3) into a shape along an elliptical closed curve (C0), and engaging portions (5a, 5b) of the externally toothed gear (3) with an internally toothed gear (2) are formed at two places, namely at both ends of the major axis (Lmax), and the engaging portions (5a, 5b) are moved in the circumferential direction. The elliptical closed curve (C0) has a non-point symmetric shape. For example, the elliptical closed curve (C0) is a line symmetric closed curve that is not symmetric about the minor axis (Lmin), and is symmetric about only the major axis (Lmax). In the non-point symmetric state, the engaging portions (5a, 5b) are formed at both ends in the major axis direction. By selecting different shapes for the engaging portions at the two locations of the major axis, vibration attributed to a secondary angular transmission error component generated along with the rotation of the wave generator (4) can be reduced.