The reduction of NO with CO and H-2 as the reductants was investigated on the rhodium-based catalyst over a temperature range of 150-400 degrees C. Micro-kinetic modelling method was utilized to compare the activities of CO and H-2. Quasi-elementary mechanisms of NO-CO and NO-H-2 consisting of 11 and 25 steps, respectively, were proposed. The reaction steps and kinetic parameters were derived from literature and some parameters were optimized to fit the experimental data. Furthermore, to verify the validity range of the developed mechanism, the reaction intermediate N2O reduction by CO and by H-2 over Rh were investigated. Over a wide range of reaction conditions, the detailed mechanism predicted experimental results quite well for both NO and N2O conversions with CO and/or H-2 as reductant. The phenomenon that NO-CO and NO-H-2 reactions commenced at similar temperature can be interpreted by the hindered H-2 dissociative adsorption steps by extensive NO adsorption. Reaction profiles such as fractional coverages, reaction pathway and sensitivity analysis provided valuable insight into the reaction systems. N2O plays a crucial role in N-2 formation for both NO-CO and NO-H-2 reaction systems. The routes involving N2O formation and decomposition were identified as the dominant pathway in N-2 formation at low temperatures.