The question of nonlinearity in the human electroencephalogram (EEG) is important, since linear methods of EEG analysis are more well-developed and computationally faster than nonlinear methods. Furthermore, the presence or absence of nonlinearity has important theoretical implications for understanding the nature of the brain's oscillatory activity. Using a linear summary measure as a control, we report a failure to reject the null hypothesis of a (largely) stationary linear-Gaussian process for normal, resting, eyes-closed EEG from a single participant. We found significant evidence of nonlinearity at two occipital sites (O1 and O2) where the 8-12.5<%0> Hz alpha rhythm was prominent. However, this element of nonlinear structure appeared trivial, as (1) we found no evidence of time irreversibility at these loci, and (2) best-fitting linear models accounted on-average for over 94% of the variance in the data with nonlinear modeling doing no better. Half of the remaining variance could be accounted for by nonstationarity. While our findings technically apply only to the one individual tested, his EEG was typical of those seen under the conditions that we employed.