Fundamental principles from structural dynamics,random theory and perturbation methods are adopted to develop a new response spectrum combination rule for the seismic analysis of non-classically damped systems,such as structure-damper systems. The approach,which is named the perturbation spectrum method,can provide a more accurate evaluation of a non-classically damped system’s mean peak response in terms of the ground response spectrum. To account for the effect of non-classical damping,all elements are included in the proposed method for seismic analysis of structure,which is usually ap-proximated by ignoring the off-diagonal elements of the modal damping matrix. Moreover,as has been adopted in the traditional Complete Quadratic Combination (CQC) method,the white noise model is also used to simplify the expressions of perturbation correlation coefficients. Finally,numerical work is performed to examine the accuracy of the proposed method by comparing the approximate results with exact ones and to demonstrate the importance of the neglected off-diagonal elements of the modal damping matrix. In the examined cases,the proposed method shows good agreement with direct time-history integration. Also,the perturbation spectrum method leads to a more efficient and economical calculation by avoiding the integral and complex operation. Fundamental principles from structural dynamics, random theory and perturbation methods are adopted to develop a new response spectrum combination rule for the seismic analysis of non-classically damped systems, such as structure-damper systems. The approach, which is named the perturbation spectrum method, can provide a more accurate evaluation of a non-classically damped system’s mean peak response in terms of the ground response spectrum. To account for the effect of non-classical damping, all elements are included in the proposed method for seismic analysis of structure, which is usually ap-proximated by ignoring the off-diagonal elements of the modal damping matrix. Moreover, as has been adopted in the traditional Complete Quadratic Combination (CQC) method, the white noise model is also used to simplify the expressions of perturbation correlation coefficients Finally, numerical work is performed to examine the accuracy of the proposed method by comparing the approximate results with exac t ones and to demonstrate the importance of the neglected off-diagonal elements of the modal damping matrix. In the examined cases, the proposed method shows good agreement with direct time-history integration. Also, the perturbation spectrum method leads to a more efficient and economical calculation by avoiding the integral and complex operation.