In this paper we investigate the modulation properties of high frequency EEG activities by delta waves during various depth of anesthesia. We show that slow and fast delta waves (0-2 Hz and 2-4 Hz respectively) and high frequency components of the EEG (8-20 Hz) are correlated with each other and there is a kind of phase locking between them that varies with depth of anesthesia. Our analyses show that maximum amplitudes of high frequency components of the EEG signal are appeared in different phases of slow and fast delta waves when the concentration of Desflurane and Propofol anesthetic agents varies in a patient. There are some slight differences in using slow and fast components of delta waves. For instance, when depth of anesthesia changes, biphasic responses of the EEG have more influences on results of the fast delta wave method. In addition, this method obtains more robust and less noisy results compared with the slow delta wave method. Since phase angle between fast EEG oscillations and delta waves indicates the status of information processing in the brain and it changes in various unconsciousness levels, it may improve the performance of other classic methods of determining depth of anesthesia.