Analysis of electroencephalogram (EEG) is presented for sleep physiology. This analysis is performed by the Instantaneous Maximum Entropy Method (IMEM), which was given by the author. Appearance and continuation of featuristic waves are not steady in EEG. The characteristics of these waves responding to epoch of sleep are analyzed. The behaviours of waves were clarified by this analysis as follows; (a) time dependent frequency of continuous oscillations of alpha rhythm was observed precisely. Sleep spindles were detected clearly within NREM and these parameters of time, frequency, and peak energy were specified. (b) delta waves with very low frequencies and sleep spindles were observed simultaneously. And (c) the relationship of sleep spindles and delta waves was first detected with negative correlation along time-axis. The analysis by the IMEM was found effective comparing conventional analysis method of FFT, bandpass filter bank, etc.