The kinetics and the mechanism of the selective reduction of nitric oxides (NOx) by hydrogen is studied on a trimetallic Pt-Mo-Co/alpha-Al2O3 catalyst under oxidising conditions. This system is interesting in view of an exhaust gas control of power plants or lean-burn cars. It can be shown that the NO dissociation is the crucial step, dominating the overall reaction behaviour and that it depends on temperature and on the partial pressure of H-2. With increasing temperatures the reaction reveals an autocatalytic behaviour resulting in bistability and hysteresis. At higher temperatures, where no bistability is found, the NO/H-2 as well as the competing O-2/H-2 reaction occur only above a certain critical partial pressure of H-2. The kinetics of the NO/H-2/ O-2 reaction are established using a modified Langmuir-Hinshelwood model (T=142 degrees C-160 degrees C, y(O2)>4%) which takes into account the critical H-2 partial pressure. The model describes the experimental data within +/-15%. The determined activation energies are: 63 kJ/mol for the NOx consumption, 77 and 45 kJ/mol for the N-2 and N2O formation, respectively, and 130 kJ/ mol for the O-2/H-2 reaction. Adsorption enthalpies are determined to -59 kJ/mol for the adsorption of H-2, -77 kJ/mol for the adsorption of NO and -97 kJ/mol for the adsorption of O-2 An interesting feature of the reaction is the enhancement of the NO/H-2 reaction by oxygen for low partial pressures of O-2 This appears to be the first study where a promoting effect of oxygen for the NO/H-2 reaction is found on a platinum supported catalyst.