In the present article, a new method is presented which attempts to identify the dynamic characteristics (eigen frequencies, eigen periods, mode shapes and modal damping ratios) of spatial asymmetric tall multi-storey buildings through measured seismic responses (accelerations). This new method is entitled ‘method of modal time-histories’, because its main target is to identify the modal time-histories of accelerations that are obtained by accelerograms recorded on the points of buildings where suitable accelerometers have been installed. In the case of an earthquake, the multi-channel local network of accelerometers records the time-histories of the accelerations of the building. In addition, in order to have a successful outcome, the instrumentation form of the multi-channel local network on the building can potentially play the most important role. This paper, first, presents a relevant mathematical analysis that is adapted to the instrumentation form applied to the multi-storey buildings and, second, outlines the new method, which consists of nine steps. Finally, in order to illustrate the theory, a suitable numerical example of an instrumented asymmetric five-storey r/c building that has been oscillated by a weak earthquake is also provided. On the one hand, the identification of the dynamic characteristics of spatial asymmetric buildings contributes to the removal of the uncertainties of building models in order to perform advanced non-linear analyses about inherent building seismic capacity. On the other hand, this method supports the simple monitoring of a building's ‘structural integrity’. Copyright © 2010 John Wiley & Sons, Ltd.