The response of a linear system to the excitation of a nonstationary random process is studied. The random excitation considered belongs to a general class which may be generated by passing a nonstationary shot noise throuh a linear filter. The behaviors of different filters are discussed. In principle the covariance and the variance functions of an arbitrary excitation process can be simulated by properly choosing a filter and a non-stationary strength function in the shot noise. It is shown that, even with a first-order filter, the variance function of a complicated process such as a typical earthquake can be well reproduced, and the determination of the structural response to such excitations becomes relatively simple.