The most convenient method to identify the dynamic characteristics such as natural periods and damping ratios of structures is to utilize the record of microtremor. Then, the method to identify them by the wavelet transforming the input and output of microtremor for a structure is presented. Using a white noise as the input of microtremor, the natural period and damping ratio of single degree of freedom system are identified. The dynamic characteristics will be changed by the reduction of stiffness of structural member during strong ground motions. These reductions of stiffness are related to the damage rate of structural members by earthquake and it is assumed that these reductions of stiffness during strong ground motion cause the abnormal signals in their responses. Then, the method of detecting these abnormal signal is proposed by utilizing the wavelet transform of the responses of structures.