The studies of the dynamic behavior of the catalytic surface, including adsorbed species, under the reaction conditions given demonstrated an approach to elucidate the mechanism of catalytic reaction, and to identify the sites where the reaction takes place on the catalyst surface. This dynamic approach revealed the adsorption-assisted processes in the kinetics of adsorption and desorption, and in some of the heterogeneous catalytic systems such as, for instance, decomposition of alcohols and formic acid. A dynamical method to identify the reaction sites on the catalyst surface was proposed. This dynamic approach was applied to the catalytic reaction of the hydrogen-oxygen reaction on silver and copper surfaces, which have different structures of chemisorbed oxygen. It was suggested that in the case of copper the reaction takes place between the peripheral part of chemisorbed oxygen islands and dissociatively chemisorbed hydrogen. On the other hand, in the case of silver the reaction proceeds between the hydrogen molecule and the middle part of the linear chain.