In this study, the nonstationary response characteristics of fixed offshore structures subjected to earthquake loadings are investigated. The nonstationarity of the earthquake excitation is modelled by introducing a time varying envelope function. The equation of motion is formulated including the nonlinear drag force of the fluid surrounding the structure. The structural responses are evaluated in terms of time dependent variance functions. Expected peak responses are also determined. Example analysis is performed for various soil condition and envelope functions using an idealized model of a fixed offshore structure in 680 ft water. The peak responses are compared with those by the conventional spectral analysis.