In this study, the problem of reliably classifying speech as normal or speech under stress is examined. It is hypothesized that speech production is composed of linear and nonlinear components, and that the nonlinear component changes measurably between normal and stressed speech. It is proposed that the Teager Energy operator could be utilized to quantify the change between normal and stressed speech. The stress styles considered are speech produced under loud, angry, Lombard effect and clear conditions. Results show that loud and angry speech can be reliably differentiated from neutral speech, while clear speech is difficult to differentiate from neutral speech. The results also show that Lombard effect speech can be reliably classified, but performance varies across speakers.