There is a complex interaction between the seismic response (i.e., peak displacements) of a nonlinear structure and the characteristics of a ground motion. One ground motion characteristic that contributes to record-to-record variability is spectral nonstationarity, or the variation of signal's frequency content with time. When the predominant natural periods of a nonlinear structure elongate in such a way as to match with the predominant frequency content in the ground motion, a phenomenon called moving resonance occurs. The effect of moving resonance on the response of nonlinear structures is investigated. Continuous complex wavelet transforms are used to examine the spectral nonstationarity of ground motion acceleration histories and associated structural displacement histories to identify the occurrences of moving resonance. A three-dimensional displacement response spectrum is used to determine which combinations of initial period and strength create the largest displacements and thus are candidate configurations for experiencing moving resonance. A method is then proposed for quantifying the effect of moving resonance on structural response. The method utilizes discrete wavelet transforms to decompose a ground motion into component signals with limited frequency band and examines the structural response due to each individual component. A discussion is provided as to how these tools can be used to identify ground motion characteristics that may be conducive to moving resonance. Copyright © 2013 John Wiley & Sons, Ltd.