A strain wave gearing which has rigid first and second internally toothed gears (101, 102), a cylindrically shaped flexible externally toothed gear, and a wave generator, the first and second internally toothed gear being disposed in parallel on an outer side of the externally toothed gear, the wave generator being disposed on an inner side of the externally toothed gear, the strain wave gearing comprising: an inner-side lubrication portion on the inner side of the externally toothed gear; an outer-side lubrication portion on the outer side of the externally toothed gear; and a lubricant-mixing-prevention part for preventing a lubricant that lubricates the inner-side lubrication portion and a lubricant that lubricates the outer-side lubrication portion from inter-mixing, wherein the inner-side lubrication portion includes sliding portions in the wave generator and a contact portion between the wave generator and an internal peripheral surface of the externally toothed gear, the outer-side lubrication portion is a tooth meshing portion between the externally toothed gear and the first and second internally toothed gears (101, 102), wherein the externally toothed gear has: a cylindrical external tooth formation portion where external teeth are formed, a first cylindrical extension portion where the external teeth are not formed, and a second cylindrical extension portion where the external teeth are not formed, the first and second cylindrical extension portion (131, 132) extending by a prescribed length in a tooth trace direction from both side ends of the external tooth forming portion, and wherein the lubrication-mixing-prevention part comprises the first and second cylindrical extension portions (131, 132), and wherein the strain wave gearing further comprises a first facing member that faces a first open end of the first cylindrical extension portion, characterised in that the strain wave gearing further comprises a second facing member that faces a second open end of the second cylindrical extension portion, the first facing member has a first annular groove, where the first open end of the first cylindrical extension portion is inserted, the second facing member has a second annular groove where the second open end of the second cylindrical extension portion is inserted, a first labyrinth seal is formed between the first cylindrical extension portion and the first annular groove, and a second labyrinth seal is formed between the second cylindrical extension portion and the second annular groove. an inner-side lubrication portion on the inner side of the externally toothed gear; an outer-side lubrication portion on the outer side of the externally toothed gear; and a lubricant-mixing-prevention part for preventing a lubricant that lubricates the inner-side lubrication portion and a lubricant that lubricates the outer-side lubrication portion from inter-mixing, wherein the inner-side lubrication portion includes sliding portions in the wave generator and a contact portion between the wave generator and an internal peripheral surface of the externally toothed gear, the outer-side lubrication portion is a tooth meshing portion between the externally toothed gear and the first and second internally toothed gears (101, 102), wherein the externally toothed gear has: a cylindrical external tooth formation portion where external teeth are formed, a first cylindrical extension portion where the external teeth are not formed, and a second cylindrical extension portion where the external teeth are not formed, the first and second cylindrical extension portion (131, 132) extending by a prescribed length in a tooth trace direction from both side ends of the external tooth forming portion, and wherein the lubrication-mixing-prevention part comprises the first and second cylindrical extension portions (131, 132), and wherein the strain wave gearing further comprises a first facing member that faces a first open end of the first cylindrical extension portion, characterised in that the strain wave gearing further comprises a second facing member that faces a second open end of the second cylindrical extension portion, the first facing member has a first annular groove, where the first open end of the first cylindrical extension portion is inserted, the second facing member has a second annular groove where the second open end of the second cylindrical extension portion is inserted, a first labyrinth seal is formed between the first cylindrical extension portion and the first annular groove, and a second labyrinth seal is formed between the second cylindrical extension portion and the second annular groove.