A novel technique for estimating the magnitude or contribution ratio of each stage backlash in a system with a two-stage gear reducer is proposed. The concept 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 the magnitude of the backlash of each stage, even though the total magnitude of the backlash 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 manufacturing machines and systems with two-stage gear reducers will become more efficient and economical by virtue of proposed technique.