Among numerous damage identification techniques, those which are used for online data-driven damage identification have received considerable attention recently. One of the most widely-used vibration-based time-domain techniques for nonlinear system identification is the extended Kalman filter, which exhibits a good performance when the parameter to be identified is a constant parameter. However, it is not as successful in identification of changes in time-varying system parameters, which is essential for real-time identification. Alternatively, the extended Kalman-Bucy filter has been recently proposed due to its enhanced capabilities in parameter estimation compared with extended Kalman filter. On the other hand, when applied as the excitation in some attractor-based damage identification techniques, chaotic and hyperchaotic dynamics produce better outcomes than does common stochastic white noise. The current study combines hyperchaotic excitations and the enhanced capabilities of extended Kalman-Bucy filter to propose a real-time approach for identification of damage in nonlinear structures. Simulation results show that the proposed approach is capable of online identification and assessment of damage in nonlinear elastic and hysteretic structures with single or multiple degrees-of-freedom using noise-corrupted measured acceleration response.