In this paper, we investigate the hippocampal and cortical sleep EEG of adult rats at different sleep stages by employing Lyapunov exponent and third-order cumulant measures to quantify and compare the chaotic and nonlinear behavior of EEG obtained during vigilance states of quiet- waking, slow-wave sleep, and rapid eye movement (REM) sleep. Lyapunov exponent was computed to characterize the EEG for chaos and third-order cumulant was used to measure the deviations from Gaussianity of the signal. Our results show positive Lyapunov exponents for all EEG states indicating a Iow- dimensional chaos for both REM and non-REM system. Furthermore, REM sleep EEG exhibits the largest Lyapunov exponent in both hippocampal and cortical EEG amongst other vigilance states. We also identified non-zero third-order cumulant for all the vigilance states which suggests their non- Gaussian behavior.