The reactivity of nitric oxide with small cobalt clusters (Co-2 and Co-3) is investigated with all electron linear combination of Gaussian type orbitals Kohn-Sham density functional theory. Full geometry optimization has been performed without symmetry constraints, starting from several initial geometries to locate different minima on the potential energy surface. Several spin configurations were considered for each case. The equilibrium geometries are characterized by their bonding energies and harmonic frequencies. A comparison with other experimental and theoretical values has been made. Bond distances, equilibrium geometries, harmonic frequencies, adduct formation energies, net atomic charges from Mulliken populations, Mayer bond orders, and ionization potentials are presented. In particular, some bridged structures are predicted. The NO molecule is molecularly bonded to Co-2(+) whereas Co-2, Co-3, and Co-3(+) show dissociative chemisorption. For Co2NO+, two low-lying states, a singlet and a triplet, are found, consistent with the deduction from experimental values that a reactive and an unreactive form are present. A comprehensive description of each adduct (ConNO) is provided. To explain the experimental behavior of these systems, we calculated the ConO2+ systems. The values of the adduct formation energies that we found are -68.7, -92.0, -81.7, and -106.9 kcal/mol for Co2NO+, Co2O2+, Co3NO+, and Co3O2+, respectively. With these results, we can conclude that ConO2+ systems are more stable than ConNO+, which provides an explanation of the experimental results.