We apply two methods (linear spectral analysis and nonlinear multifractal analysis) for analyzing the EEG records for experienced and inexperienced subjects, in meditation and background states. Through comparison of the obtained results, we show that the dominance of different rhythms (Lower Alpha vs. Upper Alpha) in different states for different types of subjects has a nonlinear nature. This is confirmed by the coincidence of spectral analysis and multi-fractal spectra analysis results, at least in the field where spectral analysis works. This opens new perspectives in applications of nonlinear methods for EEG time series study.