Adsorption, surface reaction and process dynamics on the surface of a commercial copper-based catalyst for methanol synthesis from CO/CO2/H-2 were systematically studied by means of temperature programmed desorption (TPD), temperature programmed surface reaction (TPSR), in-situ Fourier transform-inferred spectroscopy(FTIR) and stimulus-response techniques. As a part of results, an elementary step sequence was suggested and a group of ordinary differential equations (ODEs) for describing transient conversations relevant to all species on the catalyst surface and in the gas phase in a micro-fixed-bed reactor was derived. The values of the parameters referred to dynamic kinetics were estimated by fitting the solution of the ODEs with the transient response data obtained by the stimulus-response technique with a FTIR analyzer as an on-line detector.