In recognition of the increasing importance of accurate seismic vulnerability assessment, this paper deals with procedures and the application of inelastic acceleration and displacement spectra in the seismic assessment of buildings. An identification procedure is outlined, whereby an equivalent single degree of freedom (SDOF) system is devised to represent the building. The SDOF system characteristics (stiffness, strength, post-peak force response and ductility) are readily evaluated from observation of the seismic response of buildings and simple mechanics. The characteristics are then tuned using measurements from instrumented buildings. Based on the earthquake scenario and structural response characteristics, appropriate inelastic acceleration and displacement spectra are selected and used to ‘predict’ the response. Comparison between the measured and predicted responses for the five buildings studied in the paper confirm the feasibility of the procedure and the realism of the results. Copyright © 2000 John Wiley & Sons, Ltd.