A speed ratio switching type strain wave gearing (1; 100) comprising: an externally toothed gear (4; 140) including a cylinder (41; 141) capable of flexing in a radial direction, a predetermined number of first external teeth (45; 143) formed on an external peripheral surface of the cylinder (41; 141), and a predetermined number of second external teeth (46; 144) formed on the external peripheral surface of the cylinder (41; 141), the second external teeth (46; 144) being formed in a different position along an axial direction from the first external teeth (45; 143) in the external peripheral surface of the cylinder (41; 141), with the number of the first external teeth (45; 143) and that of the second external teeth (46; 144) being the same or different; a rigid first internally toothed gear (2; 110) which is disposed in a position of concentrically encircling the first external teeth (45; 143), and which includes first internal teeth (21; 111) that partially mesh with the first external teeth (45; 143); a rigid second internally toothed gear (3; 120) which is disposed in a position of concentrically encircling the second external teeth (46; 144), and which includes second internal teeth (31; 121) that partially mesh with the second external teeth (46; 144); a wave generator (5; 150) that causes the cylinder (41; 141) of the externally toothed gear (4; 140) to flex in the radial direction, causes the first external teeth (45; 143) to partially mesh with the first internal teeth (21; 111), and causes the second external teeth (46; 144) to partially mesh with the second internal teeth (31; 121); characterized in that the speed ratio switching type strain wave gearing (1; 100) further comprises a clutch mechanism (6; 160) that is able to switch one of the first internally toothed gear (2; 110) and the second internally toothed gear (3; 120), which are in a rotation-enabled state, to a rotation-disabled fixed state, the number of the first external teeth (45; 143) and that of the first internal teeth (21; 111) are different, and the number of the second external teeth (46; 144) and that of the second internal teeth (31; 121) are different. an externally toothed gear (4; 140) including a cylinder (41; 141) capable of flexing in a radial direction, a predetermined number of first external teeth (45; 143) formed on an external peripheral surface of the cylinder (41; 141), and a predetermined number of second external teeth (46; 144) formed on the external peripheral surface of the cylinder (41; 141), the second external teeth (46; 144) being formed in a different position along an axial direction from the first external teeth (45; 143) in the external peripheral surface of the cylinder (41; 141), with the number of the first external teeth (45; 143) and that of the second external teeth (46; 144) being the same or different; a rigid first internally toothed gear (2; 110) which is disposed in a position of concentrically encircling the first external teeth (45; 143), and which includes first internal teeth (21; 111) that partially mesh with the first external teeth (45; 143); a rigid second internally toothed gear (3; 120) which is disposed in a position of concentrically encircling the second external teeth (46; 144), and which includes second internal teeth (31; 121) that partially mesh with the second external teeth (46; 144); a wave generator (5; 150) that causes the cylinder (41; 141) of the externally toothed gear (4; 140) to flex in the radial direction, causes the first external teeth (45; 143) to partially mesh with the first internal teeth (21; 111), and causes the second external teeth (46; 144) to partially mesh with the second internal teeth (31; 121); characterized in that the speed ratio switching type strain wave gearing (1; 100) further comprises a clutch mechanism (6; 160) that is able to switch one of the first internally toothed gear (2; 110) and the second internally toothed gear (3; 120), which are in a rotation-enabled state, to a rotation-disabled fixed state, the number of the first external teeth (45; 143) and that of the first internal teeth (21; 111) are different, and the number of the second external teeth (46; 144) and that of the second internal teeth (31; 121) are different.