AbstractSome important types of non‐linear phenomena occuring in chemically reacting systems are explained by means of some single examples of chemical reactors. Multiple steady‐states exhibiting a distinct behavior of ignition and extinction are in the category of these phenomena. In addition all dynamic instabilities, of which there are a wide variety must also be included. These instabilities might be of thermal or purely kinetic nature, or they may result from the interaction of chemical reaction and physical transport processes. Generally these instabilities result in increasing oscillations which finally converge in stable limit cycles. The moving reaction zone which can appear in fixed‐bed reactors is described in greater detail in order to demonstrate that such a dissipative structure may be considered a prototype of an active transport process. This kind of active transport process can be observed in many systems, which are not limited just to chemical engineering. Furthermore, it is emphasized that a moving reaction zone is characterized by a certain feature which here is called “form stability”. This property might be used in order to considerably reduce the order of the non‐linear equations, describing the reactor behavior. Model reduction is of great importance with respect to both a detailed analysis of the dynamic behavior of a reactor and to the design of control concepts.