This paper addresses the problem of identification of the modal parameters for a structural system using measured non-stationary response time histories only. A Bayesian time-domain approach is presented which is based on an approximation of the probability distribution of the response to a non-stationary stochastic excitation. It allows one to obtain not only the most probable values of the updated modal parameters and stochastic excitation parameters but also their associated uncertainties using only one set of response data. It is found that the updated probability distribution can be well approximated by a Gaussian distribution centred at the most probable values of the parameters. Examples using simulated data are presented to illustrate the proposed method. Copyright © 2002 John Wiley & Sons, Ltd.