Chemical reactions carried out under strongly non-equilibrium conditions can result in a variety of interesting effects such as oscillations, chemical waves, kinetic phase transitions, bistability, instabilities and chaos - all of these effects being mathematically due to the strong non-linearities in the kinetic rate equations describing these chemical processes. The present article reviews the various types of non-linear behaviour observed in several NO reduction reactions over Pt-group metals. A large part of this review deals with oscillations and spatiotemporal pattern formation in the reaction over Rh surfaces: the reaction dynamics of this system has been realized on the microscopic, mesoscopic and macroscopic scales using field emission microscopy, photoemission electron microscopy and macroscopic rate measurements respectively. The various mechanisms of this and the other reactions reviewed in this article are also considered.