The process of NO adsorption on the cationic duster Rh-6(+) is investigated using the density-functional theory (DFT) with the generalized gradient approximation (GGA) to exchange and correlation. We determine the geometries, electronic structure, and relevant energies for different structural and spin isomers of Rh-6(0,+/-), and we study the consecutive adsorption of two NO molecules on the cationic cluster Rh-6(+). With regard to the first NO molecule, different adsorption energies are found for the ground state octahedral structure of the bare cationic cluster and for the first isomer, which, having a prism-type structure, undergoes a structural transition to an octahedral symmetry upon dissociative adsorption of NO. Several dissociative NO adsorption processes are analyzed in comparison with molecular adsorption of NO to give support to the first step of the reaction inferred from experiments. With regard to the adsorption of a second NO molecule, the intermediate with lowest energy contains a preformed N-2 molecule. The energy of that complex is about 0.7 eV smaller than the sum of the free N-2 energy plus the lowest energy of the Rh-6(+)-O-2 complex. This complex is composed of two separated O atoms occupying adjacent 2-fold bridging positions of the nearly undistorted Rh-6(+) octahedral cluster. These findings are in qualitative agreement with experiments.