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Interhemispheric differences in the EEG of nine healthy right-handed human subjects (C3 vs. C4 derivations) were investigated during resting wake with closed eyes (CE) and sleep stages I, II, III, IV and REM. The harmonic power spectral density within the EEG main spectral bands, the fractal (Dr) and the correlation (D
2) dimension as well as the largest Lyapunov exponent (
λ
1) of both hemispheres were compared. In addition, the relationships between non-linear and spectral measures were analyzed. Dr, D
2,
λ
1 and the power in alpha band exhibited interhemispheric differences during waking, the values from the right hemisphere (RH) being higher than those of the left (LH) except for
λ
1. During slow wave sleep (SWS), non-linear parameters detected opposite EEG asymmetries (D
2 in stage III and
λ
1 in stage IV) to those found in the other behavioural stages. In addition, both D
2 and
λ
1 were correlated (negatively) with the power in the delta band, but
λ
1 was also correlated (positively) with the power in the alpha and beta bands. In conclusion, RH appears to be more complex though more predictable than the LH during CE and sleep stages I and II, these characteristics changing to the LH during SWS.