A flat strain wave gearing (1) has a mechanism for preventing a flexible externally toothed gear (4) from moving in the direction of the device center axis (1a) with respect to a rigid internally toothed gears (2, 3). The mechanism has an inner-peripheral groove (11) formed on inner teeth (3a) of the internally toothed gear (3), an outer-peripheral groove (12) formed on outer teeth (4a) of the externally toothed gear (4), and a flexible ring (13) mounted between the inner-peripheral groove (11) and the outer-peripheral groove (12). The ring (13) is engageable with groove inner-peripheral surfaces (11a, 11b, 12a, 12b), from the direction of the device center axis (1a), at meshing positions of the both gears (2, 4).