Burst suppression electroencephalograms from 9 comatose patients have been studied using nonlinear dynamic techniques. These EEG records show many dynamical features characteristic of nonlinear systems, including sensitive dependence on initial conditions, self-organization, similarity across scales, and intermittency. Histograms of burst durations showed an asymmetric distribution with a decreasing tail of increasing duration. Interpreting the histograms from the standpoint of intermittency classifications of iterated dynamical maps, the absence of any conspicuous maximal cut-off duration suggests a type III intermittency. The power-law exponent of the decreasing tail is -3/2 for type III intermittency in the large scale sample size limit, and we have found the EEGs to be consistent with type III intermittency behavior. We have also developed a nonlinear algorithm which models burst suppression pattern based on a low dimensional return map. Burst suppression pattern appears to be the constrained activity of a nonlinear dynamical system at the transition to chaos.