Abstract: It is not any single maximum value, but the whole process of the ground motion that determines the behavior of a structure during a strong earthquake. Statistical characteristics of the whole process or the time history of ground motion are functions of earthquake magnitude and propagation path and media, especially soil condition near ground surface. Since there exist some potentially reliable method to calculate ground surface motion from bedrock motion, reasonable evaluation of bedrock motion parameters and generation of time histories therefrom seem to become more important.The present paper analysed records obtained on 27 U. S. stations on bedrocks, trying to find out some statistical functional relations of the acceleration response spectra and some maximum values with earthquake magnitude and distance which are the most important basis for generating time history of ground motion.