A strain wave gearing comprising: a rigid first internally toothed gear in which first internal teeth are formed; a rigid second internally toothed gear in which second internal teeth are formed, the second internally toothed gear being disposed so as to be coaxially aligned in parallel with the first internally toothed gear; a flexible externally toothed gear in which first external teeth capable of meshing with the first internal teeth and second external teeth capable of meshing with the second internal teeth are formed in the outer-peripheral surface of a radially flexible cylindrical body, the second external teeth differing in number from the first external teeth, and the externally toothed gear being disposed coaxially inside the first and second internally toothed gears (2, 3); and a wave generator which causes the externally toothed gear to flex in an ellipsoidal shape, causing the first external teeth to partially mesh with the first internal teeth and causing the second external teeth to partially mesh with the second internal teeth; wherein the wave generator has: a rigid plug; an ellipsoidally contoured outer-peripheral surface formed in an outer-peripheral surface of the plug; a first wave bearing fitted to the outer-peripheral surface, the first wave bearing comprising ball bearings for supporting the first external teeth; and a second wave bearing fitted to the outer-peripheral surface, the second wave bearing comprising ball bearings for supporting the second external teeth, wherein, where m 1 is a module of the first external teeth, m 2 is a module of the second external teeth, n 1 and n 2 are positive integers, 2n 1 is a difference in number of teeth between the first external teeth and the first internal teeth, and 2n 2 is a difference in number of teeth between the second external teeth and the second internal teeth, a theoretical value d 1 of an amount by which the first external teeth are radially flexed at major-axis positions and a theoretical value d 2 of an amount by which the second external teeth are radially flexed at major-axis positions when the externally toothed gear is flexed in an ellipsoidal shape are respectively represented by relationships d 1 = m 1 n 1, d 2 = m 2 n 2; radial flexing amounts d 1a and d 2a satisfy relationships d 1 a = ωd 1, and d 2 a = ωd 2, where d 1a is an average radial flexing amount by which the first external teeth are radially flexed by the wave generator, d 2a is an average radial flexing amount by which the second external teeth are radially flexed by the wave generator, and ω is a coefficient having a value more than 1. a rigid first internally toothed gear in which first internal teeth are formed; a rigid second internally toothed gear in which second internal teeth are formed, the second internally toothed gear being disposed so as to be coaxially aligned in parallel with the first internally toothed gear; a flexible externally toothed gear in which first external teeth capable of meshing with the first internal teeth and second external teeth capable of meshing with the second internal teeth are formed in the outer-peripheral surface of a radially flexible cylindrical body, the second external teeth differing in number from the first external teeth, and the externally toothed gear being disposed coaxially inside the first and second internally toothed gears (2, 3); and a wave generator which causes the externally toothed gear to flex in an ellipsoidal shape, causing the first external teeth to partially mesh with the first internal teeth and causing the second external teeth to partially mesh with the second internal teeth; wherein the wave generator has: a rigid plug; an ellipsoidally contoured outer-peripheral surface formed in an outer-peripheral surface of the plug; a first wave bearing fitted to the outer-peripheral surface, the first wave bearing comprising ball bearings for supporting the first external teeth; and a second wave bearing fitted to the outer-peripheral surface, the second wave bearing comprising ball bearings for supporting the second external teeth, a rigid plug; an ellipsoidally contoured outer-peripheral surface formed in an outer-peripheral surface of the plug; a first wave bearing fitted to the outer-peripheral surface, the first wave bearing comprising ball bearings for supporting the first external teeth; and a second wave bearing fitted to the outer-peripheral surface, the second wave bearing comprising ball bearings for supporting the second external teeth, wherein, where m 1 is a module of the first external teeth, m 2 is a module of the second external teeth, n 1 and n 2 are positive integers, 2n 1 is a difference in number of teeth between the first external teeth and the first internal teeth, and 2n 2 is a difference in number of teeth between the second external teeth and the second internal teeth, a theoretical value d 1 of an amount by which the first external teeth are radially flexed at major-axis positions and a theoretical value d 2 of an amount by which the second external teeth are radially flexed at major-axis positions when the externally toothed gear is flexed in an ellipsoidal shape are respectively represented by relationships d 1 = m 1 n 1, d 2 = m 2 n 2; radial flexing amounts d 1a and d 2a satisfy relationships d 1 a = ωd 1, and d 2 a = ωd 2, where d 1a is an average radial flexing amount by which the first external teeth are radially flexed by the wave generator, d 2a is an average radial flexing amount by which the second external teeth are radially flexed by the wave generator, and ω is a coefficient having a value more than 1.