Abstract: Utilizing the amplitude and phase of continuous wavelet transform (CWT) coefficient on ridge, weak nonlinearities on damping and stiffness are identified from the free decay response of a structural system in this paper. A new algorithm for the detection of ridge is introduced to eliminate the frequency-shift of CWT amplitude extreme. In order to minimize end-effect, the parameter selection of wavelet function is performed by using an optimization technique based on the fitting error of least squares. Both numerical and experimental studies are performed to demonstrate the proposed procedure and verify its accuracy. The experimental system is a high accuracy instrument for measuring moment of inertia. The results show the method works very well in identifying weak nonlinearities on damping and stiffness of structures.