The assumption and problem of the modesuperposition response spectrum method in seismic design code is discussed based on a brief review of the development of the seismic design method for building structures. The scope of application for the classical damping theory is analyzed and the necessity of the research on mode-superposition method for non-classical damping is presented. The progresses on the mode superposition response spectrum theory are discussed. This includes: 1) the complex mode superposition method (in real form) for the non-classically damped linear system and the general calculation formula for the application of code; 2) the complex complete quadratic combination (CCQC) method for the non-classically damped linear system, which is based on the same assumptions as in deducing the complete quadratic combination (CQC) method which is popularly used in seismic design codes of many countries; 3) the complex complete quadratic combination with three components (CCQC3) method, which is a generalization of the CCQC method to the case of multi-components and multiple-support seismic excitations and deducing corresponding method; 4) the approach for calculation of seismic response of the non-classically damped system with overcritical damping and the calculation method of seismic response for the linear system with multiple eigenvalues; 5) the time-dependent CCQC(t) algorithm considering nonstationary earthquake ground motion; 6) an applied and effective method to solve the low order complex vector basis for the large linear non-classically damped system, which can be expediently used in practice to avoid the unknown errors coming from the forced uncoupling method; 7) bringing forward the concept of partial quadratic combination in order to reduce the calculation amount of CQC and CCQC methods, and studying the primary estimation-criterion. The reasonability and applicable scope of these methods are also briefly discussed in this paper.Keywords non-classical damping, complete quadratic combination method, complex complete quadratic combination method, multi-component and multiple-support seismic excitations, overcritical damping, multiple eigenvalues 1 State-of-the-art of seismic design methods based on mode superpositionThe seismic design methods based on dynamic theory can be classified into two types, such as mode-superposition response spectrum method and time history approach. Principally, response-spectrum mode superposition method is only appropriate for designing and analyzing seismic responses in an elastic state, whereas the time history approach is suitable both for elastic and plastic response analyses. In the last 20 years, the performance-based design methodology with multiple protection levels corresponding to different design earthquake has been internationally recognized. Actually, in China, such kind of design philosophy has poured into seismic design code for buildings, GBJ11-89, published in 1989, and is divided into three levels, i.e., minor earthquake with return period of 50 years...
