A unique technique to estimate the magnitude or contribution ratio of each stage backlash in a system with a two-stage gear reducer is proposed. The concept to estimate the magnitude or contribution ratio of each stage backlash is based on the change of frequency response characteristic, in particular, the change of anti-resonant frequency and resonant frequency, due to the change of each stage backlash magnitude, even though the total backlash magnitude of a system with a two-stage gear reducer is constant. The validity of the technique is verified in a seeker gimbal and satisfactory results are obtained. It is thought that the diagnosis and maintenance of the manufacturing machines and systems with two-stage gear reducers will become more efficient and economical by virtue of the proposed technique.