Nonlinear structures, when subjected to multiple ground motion records that are scaled to consistent ground motion intensity show significant variation in their response. This effect of ground motion randomness on the variation of structural response is defined as Record-to-Record (RTR) Variability. Ground motion characteristics that contribute to this variability in response includes the variation of signal composition (frequency content) with time (spectral nonstationarity).The phenomenon of moving resonance which occurs when the frequency content of the ground motion shifts in a similar manner as the natural frequencies of the structural response, is likely a contributor to variability. This brings the need to further understand the sources of variability due to moving resonance. The present study was carried out to develop a method to analyze the time-frequency content of a ground motion to assess the occurrence of moving resonance and to quantify its potential in effecting the structural systems. Bilinear elastic and elastoplastic hysteretic behavior was considered. Detailed analysis is done to quantify the effect of moving resonance on structural systems due to 22 far field ground motion records. The wavelet coefficient plots gave very good detail of the characteristics of the ground motions that were not clear from the acceleration time histories and response spectra plots. Instances of moving resonance were found out to be significant. Amplification due to moving resonance was found to be quite large. One instance studied in detail (accelerogram of Northridge earthquake at Beverly Hills) had peak displacement amplified by 6 times compared to the amount of peak displacement expected if the system did not exhibit moving resonance. Based on the analyses results, the characteristics of the ground motion records that don't cause significant moving resonance effect on structural systems were observed. Similarly, the characteristics of the ground motions that do cause moving resonance effect on structural systems were examined. / Master of Science