The human-machine system behavior and performance are dynamic, nonlinear, and possibly chaotic. Various techniques have been used to describe such dynamic and nonlinear system characteristics. However, these techniques have rarely been able to accommodate the chaotic behavior of such a nonlinear system. Therefore, this study proposes the use of nonlinear dynamic system theory as one possible technique to account for the dynamic, nonlinear, and possibly chaotic human-machine system characteristics. It briefly describes some of the available nonlinear dynamic system techniques and illustrates how their application can explain various properties of the human-machine system. A pilot's heart interbeat interval (IBI) and altitude tracking error time series data are used in the illustration. Further, the possible applications of the theory in various domains of human factors for on-line assessment, short-term prediction, and control of human-machine system behavior and performance are discussed.