The focus of this work is on methods for modal identification of civil structures using output data only. An important family of time domain methods uses autoregressive time series models and exploits formulations developed in the field of system control. Another strategy consists of using methods well tested in the identification of structures on the basis of impulse response or free decay and extending them to the analysis of response signals generated by excitations of a more general nature. A third option refers to the Ho-Kalman minimal realization algorithm, which was extended by Akaike and Aoki to stochastic systems. These approaches, or their combinations, include a sizable proportion of the methods actually used in output-only identification of civil structures subjected to natural excitation, and most of them are based on stationarity assumptions. The question that prompted this study was as follows: what degrees of reliability and accuracy can such methods ensure when they are used, as is often the case in actual practice, in nonstationary conditions? An answer to this question was sought numerically by focusing on nonstationary conditions deemed typical of the actions naturally applied to civil structures.