A strain wave gearing comprising: a rigid first internally toothed gear formed with first internal teeth; a rigid second internally toothed gear formed with second internal teeth, 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 an outer-peripheral surface of a radially flexible cylindrical body, the second teeth differing in number from the first teeth, and the externally toothed gear being disposed coaxially inside the first and second internally toothed gears (2, 3); and a wave generator for flexing the externally toothed gear in an ellipsoidal shape to cause the first external teeth to partially mesh with the first internal teeth and to cause the second external teeth to partially mesh with the second internal teeth, wherein first and second rim wall thicknesses t and t are set to have values that satisfy 0.5 < t 1 / t 2 < 1.0, where the first rim wall thickness t is a rim wall thickness of a tooth bottom rim of the first external teeth, and the second rim wall thickness t is a rim wall thickness of a tooth bottom rim of the second external teeth; and characterized in that radial flexing amounts by which the first and second external teeth (7, 8) are flexed respectively by the wave generator are set to be a same radial flexing amount d; and the same radial flexing amount d satifies the relationship d = d 1 + d 2 / ω, 1.4 ≦ ω ≦ 2.6, 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, and 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 when the external teeth are flexed in an ellipsoidal shape are respectively represented by d 1 = m 1 n 1 and d 2 = m 2 n 2; wherein, a relationship Zf 1 = Zf 2 − 2 n is satisfied, where Zf1 is a tooth number of the first external teeth, Zf2 is a tooth number of the second external teeth, and n is a positive integer. a rigid first internally toothed gear formed with first internal teeth; a rigid second internally toothed gear formed with second internal teeth, 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 an outer-peripheral surface of a radially flexible cylindrical body, the second teeth differing in number from the first teeth, and the externally toothed gear being disposed coaxially inside the first and second internally toothed gears (2, 3); and a wave generator for flexing the externally toothed gear in an ellipsoidal shape to cause the first external teeth to partially mesh with the first internal teeth and to cause the second external teeth to partially mesh with the second internal teeth, wherein first and second rim wall thicknesses t and t are set to have values that satisfy 0.5 < t 1 / t 2 < 1.0, where the first rim wall thickness t is a rim wall thickness of a tooth bottom rim of the first external teeth, and the second rim wall thickness t is a rim wall thickness of a tooth bottom rim of the second external teeth; and characterized in that radial flexing amounts by which the first and second external teeth (7, 8) are flexed respectively by the wave generator are set to be a same radial flexing amount d; and the same radial flexing amount d satifies the relationship d = d 1 + d 2 / ω, 1.4 ≦ ω ≦ 2.6, 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, and 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 when the external teeth are flexed in an ellipsoidal shape are respectively represented by d 1 = m 1 n 1 and d 2 = m 2 n 2; wherein, a relationship Zf 1 = Zf 2 − 2 n is satisfied, where Zf1 is a tooth number of the first external teeth, Zf2 is a tooth number of the second external teeth, and n is a positive integer.