This paper examines the effect of structural damage on the practical/computational identifiability of the parameters that define nonlinear models of building structures subjected to earthquake-induced base motions. The objective is to determine the level of physical damage expected to successfully estimate the nonlinear parameters of restoring force models. For this purpose, the analyses aim to determine if the parameters that define a hysteretic (Bouc-Wen type) model can be identified within a predefined level of accuracy from accelerations measured during seismic events that cause minor damage. The identified model is then interrogated to determine if it can provide accurate predictions of the response and damage level experienced during strong ground motions that cause moderate-to-severe damage. The damage model adopted is a Park–Ang type model and the unscented Kalman filter is used for parameter estimation. The results are verified using simulated two-dimensional building models and validated using experimental data from a large-scale shake table test.