The dynamical system with local nonlinearity induced by the contact with outside subjects was studied. The harmonic components including the superharmonic components were investigated. The relationship between the superharmonic components of the system response and the frequency response matrix of the linear system was revealed. Then, a simple and fast nonlinearity position identification method was presented. Using this method, the nonlinearity position can be identified based on only two vibration responses of the system and only one time harmonic excitation. Numerical studies on a MDOF(MultiDegree of Freedom) massspringdamping system was carried out to show the efficiency of the presented identification method.