A systematic density functional theory study using periodic models is presented concerning the chemisorption of CO and NO on various sites of RhCu(111) surfaces. The properties of the adsorbed molecules on various mono- and bimetallic sites of these alloy surfaces have been obtained and compared to those corresponding to the pure Rh(111) and Cu(111) surfaces. It is shown that that the interaction of small probe molecules such as CO or NO on RhCu alloys is essentially dominated by the atomic nature of the surface active site with little influence of the rest of the metallic system. Moreover, it is suggested that it is possible to control the adsorption site of these molecules by appropriate choice of the surface composition.