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In seismic design codes of practice,response spectra are generally presented without including any load history;hence the nonlinear analysis of structures based solely on conventional earthquake response is not theoretically sound,particularly for long-period tall buildings.In this paper,a concept of seismic damage evolution is introduced and the method of analysis for characterising the process of seismic damage to structures under earthquakes is presented.Damage evolution spectra for seismic analysis of tall buildings are then developed as an effective means of describing and simplifying earthquake ground motions.These spectra are shown to be very useful in selecting the ground motion-time history and,particularly,validating the equivalent static-load analysis and design of high-rise buildingsnear-fault pulse-like ground motions.Numerical study of the seismic inelastic performance of a vertically irregular tall building is conducted with consideration of the seismic damage evolution spectra.