The analysis of the effects of soil-structure interaction on the response of structures during strong earthquake ground motions are presented. The possibility of estimating the rocking motion of the foundation is examined through geometrical analysis of recorded motions. The records obtained during the San Fernando and the Lytle creek earthquakes are utilized to estimate the rocking of the foundations of Millikan Library as well as the translation of the building at the roof relative to a moving frame of reference attached to the foundation. Through these estimates and using the appropriate transfer functions the modal frequencies of the structure and those of the complete soil-structure system are identified.; An experimental approach for estimating the impedance functions of the foundation is explored and the horizontal and rocking compliances are estimated for the foundation of Millikan Library. Comparisons of the results with those obtained from analytical studies are presented.; The possible contribution of the hysteretic damping to the response of a simple mathematical model of a soil-structure system is examined. The response of Millikan Library to the forced-vibration testes is used to test the model through an attempt to reproduce the experimental observations.