Many analyses of the EEG signal using frequency decomposition methods rest on the assumption that the fundamental signal-generating process has stochastic properties (i.e., no long-range temporal correlations, or temporal self-similarity). In this paper, the detrended fluctuation analysis (DFA) algorithm of Peng et al. (1992) was used to determine whether the locally-detrended EEG contained long-range correlations, indicating fractal structure, or whether it was best characterised as a stochastic random-walk process. If the EEG was generated by a random walk process, then an estimated scaling parameter was predicted to be =0.5, whereas the scaling parameter for a fractal process would lie in the range 0.5< 1.5. In this study, highly significant departures from =0.5 were observed from an ensemble of 32 EEG signals, ()=1.26, =0.06, indicating that the EEG samples could not have been generated by a random walk process. This result also suggests that the EEG is generated by a fractal process which contains long-range temporal correlations of the order 1/f^1.52.