In this paper, we tested the Gaussianity of the sleep EEG at each sleep stages. The test statistics we used are mainly bicoherence statistic and Kolmorgov-Smirnov statistic additively. We selected every five pages of each stage, which represent the specific stage. We apply the test to those pages. Then, we also applied the test to all the pages of sleep. The results shows that the EEG of every stage except SWS (slow wave sleep) can be accepted as Gaussian process. Comparing the result of representative data of each stage with that of the total pages of each stages, except SWS, some difference is founded. It means that the inter-variability of each stage except SWS is large. We think that it is due to the smoothing rules of R and K between obscure stages.