Base isolation systems have been used in buildings and bridges as protective systems against earthquakes, and the health monitoring of base isolators is of great importance. The ability to detect damages on-line, based on vibration data measured from the health monitoring system, will ensure the reliability and safety of base-isolated structures. When a base-isolated structure is subject to strong earthquakes, it is important to be able to determine the damage of isolators from the seismic response data either on-line or almost on-line. The problem is quite challenging because the restoring force of the base isolator is inelastic, and only a limited number of sensors can be installed in the structural health monitoring system, indicating that the response data may not be available at all degrees of freedom of the structure and that the external excitations may not be measured. In this paper, we propose a new data analysis method, referred to as the sequential nonlinear least-square estimation with unknown inputs and unknown outputs (SNLSE-UI-UO), for the real time on-line identification of structural damages, including the nonlinear base isolators. In this approach, only a limited number of response data are needed and the external excitations may not be measured. Analytical recursive solutions are derived and presented, which are not available in previous literature. The Bou-Wen model is used for the nonlinear base-isolation system, and the accuracy of the new approach is demonstrated using a base-isolated building. Simulation results demonstrate that the proposed approach is capable of tracking on-line the changes of structural parameters, such as the parameters of base isolators, leading to the identification of structural damages.