The simplest approach in studying the response of a structural system to an external dynamic excitation is to idealize the system as a linear singledegree-of-freedom (SDOF) system comprising a mass body, a spring representing the system stiffness and a dashpot representing the energy dissipation mechanism of the system. In many of the cases, the dynamic excitation to which the system is subjected is a seismic ground motion process. The seismic motions are known to be highly nonstationary with time-varying statistical characteristics and are also characterized by timedependent frequency content due to the dispersion of the constituent waves. Different solution procedures have been proposed to obtain the nonstationary system response; however, the specific modulating functions used in the approach determined the nature of the nonstationarity to be considered in the analysis. Moreover, the time-varying frequency content of input excitations has not been considered. With the development of the wavelet-based analytical technique, it has become possible to tackle the frequency nonstationarities as well. In this chapter, we will see how to use the discretized version of the continuous wavelet transform to obtain the nonstationary response of a SDOF system subjected to seismic ground motion excitation. The basic idea to solve system equations of motion in the wavelet domain is clearly explained in this chapter.