The previous chapters have been devoted to the response analysis of linear systems subjected to nonstationary random vibrations. In these chapters, the basic idea of wavelets and the usefulness of wavelet-based analysis have been explained. The theory of wavelet-based analysis is used to develop and formulate the system equations of motions and transfer those to the wavelet domain and solve using wavelet coefficients. However, not all the structures behave in a way that could be well approximated by a linear system. In reality, the responses of a structure may deviate far from linear considerations [34-38]. The response of, say, buildings to earthquakes is a nonlinear dynamic problem. The readers should keep in mind that at this point we are talking about the nonlinearity present in the material model of the structure. However, it should also be borne in mind that we are not concerned about how to represent material nonlinearity; rather, we are focused only on how to formulate the equations of motion once we consider nonlinearity in our assumptions and how we solve the system dynamics using the wavelet analytical technique. The basic background theory regarding wavelets as discussed in previous chapters is used in this chapter too; however, the problem has become more complicated due to introduction of nonlinearity into the system. The main objective is to provide an insight into the formulation of the problem related to obtaining the nonlinear response of the system using the wavelet-based approach.