A formulation for the response of the secondary systems subjected to multicomponent earthquake acceleration has been developed, using the random vibration theory. The method accounts for interaction between the primary and the secondary systems as well as the nonproportionality of the combined primaryseondary system damping. The required formulations for the calculation of the autocorrelation function, the power spectral density function, the response spectrum and the critical angle have been obtained. The formulation has been arranged in such a way that the floor response spectrum can be calculated directly from the earthquake response spectra of multicomponent input. The floor response spectra of torsional frames subjected to average response spectrum of 20 earthquake records of Iran have been calculated. Variations of the spectra to various structure parameters such as eccentricity, mass ratio, and nonproportional damping have been studied. Results show that for large eccentricities the effect of multicomponentness of earthquake becomes important and can not be neglected.