Structural health monitoring of large multispan flexible bridges is particularly important because of their important role in civil infrastructure and transportation systems. In this study, the response of the Yokohama Bay Bridge (YBB), a three-span cable-stayed bridge, to the 2011 Great East Japan Earthquake is used to perform multi-input multi-output system identification studies. The extensive multicomponent measurements are also used to develop and validate data-driven nonlinear mathematical models that can predict the response of YBB to various earthquake records and can accurately estimate its damping characteristics when the system is driven into the nonlinear response range. A combination of least-square (parametric) and neural network (nonparametric) approaches is used to develop the mathematical models, along with time-marching techniques for dynamic response calculations. It is shown that the nonlinear mathematical models perform better than the equivalent linear models, both for response prediction and damping estimation. The importance of having an accurate approach for quantifying the damping due to the variety of nonlinear features in the YBB response is shown. This study demonstrates the significance of constructing robust mathematical models that can capture the correct physics of the underlying system and that can be used for computational purposes to augment experimental studies. Given the lack of suitable data sets for full-scale structures under extreme loads, the availability of the long-duration measurements from the 2011 Great East Japan Earthquake and its many strong aftershocks provides an excellent opportunity to perform the analyses presented in this study. Copyright (c) 2013 John Wiley & Sons, Ltd.