We report a density functional theory investigation of the adsorption properties of CO, NO, and OH on the Cu-13, Pt7Cu6, and Pt-13 clusters in the cationic, neutral, and anionic states with the aim to improve our atomistic understanding of the adsorption properties on bimetallic clusters compared with monometallic clusters. The adsorption energy of CO and NO are substantially stronger on Pt-13 than on Cu-13, and hence, CO and NO bind preferentially on Pt sites on Pt7Cu6. Thus, it can contribute to drive the migration of the Pt atoms from the core to the surface region in large PtCu nanoalloys. The CO and NO adsorption energies on the bimetallic cluster are enhanced by a few percent compared with the energies of the monometallic clusters, which shows that the Pt-Cu interaction can contribute to an increase in the adsorption energy. In contrast with CO and NO trends, the OH adsorption energies on Cu-13, Pt7Cu6, and Pt-13 deviates only up to 0.31 eV, and hence, there is no clear preference for Cu or Pt sites on Pt7Cu6 or an enhancement of the adsorption energy on the bimetallic systems. We found a reduction of the CO and NO vibrational frequencies upon adsorption, which indicates a weakening of the CO and NO binding energies, and it is supported by a slight increase in the bond lengths. However, the OH vibrational frequency increases upon adsorption, which indicates an enhancement of the OH binding energy, which is supported by a slight decrease in the bond length by about 0.01 a. It can be explained by the large charge transfer from the clusters to the O atom, which enhances the electrostatic interaction in the O-H bonding.