A strain wave gearing is lubricated by a non-hydrophobized powder enclosed in an internal space until the strain wave gearing is fully broken in, and the non-hydrophobized powder is transferred to contact surfaces of contact parts to form a lubricating film. During operation under load, the strain wave gearing is lubricated by a hydrophobized powder enclosed in the internal space instead of the non-hydrophobized powder. Each of the powders used is a powder of an ionic crystalline compound (MoS2, WS2, etc.) having a layered crystal structure. By lubricating the strain wave gearing with the hydrophobized powder during operation under load, any temporary decrease in efficiency at the start of operation is minimized and stable operation of the strain wave gearing can be maintained.