The Chi-Chi earthquake supplied us unprecedented information on near-fault ground motions and made it possible to study the randomness of near-fault ground motions in assembly. From the viewpoint of random function, response spectra of 30 stations under similar conditions are used as the samples of three random functions. The mean value functions, autocorrelation, and cross-correlation matrixes of response spectra are studied. According to this study, the response spectra of three components are all the nonstationary functions. The spectra characteristics of two horizontal components are similar in statistical meaning, but there are certain differences in randomness. There are considerable differences between randomness of response spectra of vertical component and horizontal components. It can be seen that during the period range from 0.1 to 4 sec, which is the most commonly investigated period range in engineering practice, the autocorrelation and cross-correlation matrixes of response spectra of two horizontal components have roughly diamondlike shapes; however, it is not the case for the autocorrelation matrixes of vertical component and cross-correlation matrixes of vertical to horizontal components, which are irregular in general. In this article, a primary mathematic model is established to simulate the autocorrelation matrixes and cross-correlation matrixes of response spectra of two horizontal components, which paves a way for further study in the randomness of response spectra.