Continuation methods combined with the concepts of stability and bifurcation theory are now widely accepted far the analysis of chemical engineering systems. Nonlinear analysis can lead to an improved process design or process operation. The integration of continuation methods into standard tools for dynamic process simulation opens a wide range of possible applications in chemical engineering. The first part of this paper gives a basic introduction into nonlinear dynamics. In the second part, that theory is applied to three different types of chemical engineering processes, which have been studied recently at the Institut fur Systemdynamik und Regelungstechnik of the Universitat Stuttgart.