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The purpose of this study is to verify that EEG is composed of frequency components with chaotic characteristics. EEG data are decomposed into frequency components, and then the chaos and fractal analyses are applied. More precisely, the running spectrum of EEG is derived and the chaos analysis is applied evaluating the Lyapunov spectrum and the correlation dimension. As a result, the existence of the chaotic phenomenon is found for most of the frequency components used as the objects of the analysis. It is also found that the fractal properties exist in most of the frequency components. The multifractal analysis is applied to the EEG data, and the q-th order generalised dimension is evaluated. It is seen as a result that the reconstructed attractors of EEG are characterized by a nonuniform fractal distributions, which are represented by a large number of scaling indices concerning with the dimension.