Methods for analysis of nonstationary EEGs, that is, EEGs whose patterns undergo changes with time (e.g., alpha blocking, paroxysmal slow waves, onset of drowsiness/sleep, but excluding spikes/sharp waves) are reviewed. The concepts of stationarity and nonstationarity, and general techniques for their evaluation, are discussed. Simpler methods for monitoring for nonstationarity include running determinations of average amplitude and average period or interval. Piecewise stationary analysis includes characterization, by spectra obtained by fast Fourier transform or by autoregressive modeling, of sections of EEGs preselected to be stationary. In Kalman filtering, the autoregressive model itself becomes time-varying. Segmentation of the EEG into stationary lengths can be carried out on a fixed-interval basis (i.e., of successive, e.g., l-s intervals), with clustering (grouping) or classification according to the features (e.g., spectra) of each interval, and concatenation of adjacent similar intervals. Alternatively, in adaptive (variable-interval) segmentation, the EEG is continuously monitored automatically for any significant departure from stationarity, and segment boundaries are placed accordingly. A number of applications of the various methods are included, with examples of succinct summary displays. Problems and prospects are discussed.