The present investigation develops methods for the identie cation of highly localized structural damages in nonlinear structures. The damage is dee ned as either a reduction of stiffness or a change of restoring force characteristics from linear (undamaged state ) to weak nonlinear (damaged state ). One method for identifying both the location and type of damages is the location vector method (LVM). The other method is for quantifying the damage. The LVM requires only the modal data from the e rst few fundamental modes. The second method is based on fast Fourier transform (FFT) and the least-squares method under the assumptions that the location of the damages can be identie ed and their responses can be measured by testing. Without loss of generality, the methods are illustrated by a e ve-degree-of-freedom Dufe ng’ s nonlinear system. Measurement data are simulated in the time domain and in the frequency domain by using the Runge ‐Kutta method and FFT, respectively. The robustness and effectiveness of the methods are examined by using a simulated output time history contaminated by a 5% white noise, which represents more realistic levels of measurement errors.