System identification techniques has been extensively developed during the past twenty years mostly because of a large number of applications in diverse fields like electric power systems, hydrology, aeronautics, astronautics, mechanical engineering and structural engineering. However, most of the techniques developed so far are based on the assumption that the structural systems to be identified are linear while, in practice, most engineering structural systems may be nonlinear, especially for those structures damaged because of loadings, material degradation, environmental reasons and others. It is therefore necessary to extend existing linear system identification techniques, or to develop new techniques into the nonlinear structural systems so that the structural damages, defined as stiffness reduction of local elements or element characteristics changing to nonlinear, can be detected, located and quantified. The objective of the present study is to first develop analytical methods for structural systems with local nonlinear elements. Then the behaviors of such systems under periodical, impulse and random excitations are investigated. Next, given a structural system with a changing local member, stiffness reduction and/or linear to nonlinear, the effects on the responses under the given excitation are investigated. Furthermore, the study is extended into the identification of the locations of the changing elements. Various methodologies are investigated and their results are compared. These methods include the Fast Fourier Transform and Wavelets Transform. This is followed by the methodology development for the quantification of the structural parameter changes which has the direct application in structural damage estimation. The developed methods are applied to both linear and nonlinear cases.