In a strain wave gearing, external teeth of a flexible externally toothed gear are elastically deformable in a direction in which the tooth thickness of the external teeth decreases. Engagement between internal teeth of a first and a second rigid internally toothed gears and the external teeth is set in an overlapping state in which the external teeth elastically deform and engage in a state in which no gap is present. The tooth profile of the internal teeth is a corrected tooth profile so that no interference occurs between a tooth top portion of the internal teeth and a dedendum portion of the external teeth when the teeth are engaged in the overlapping state. A strain wave gearing capable of minimizing or eliminating tooth engagement backlash is realized.