The stationary points on the potential energy surfaces (PES) of cobalt oxide clusters were studied by the density functional theory, with the B1LYP exchange-correlation functional. A number of local minima were detected on the doublet, quartet, and sextet PES of CoOn (n = 1-4) and the singlet, triplet, and quintet PES of the corresponding anions. The normal vibrations of all optimized structures were calculated and interpreted in terms of group theory. The global minima and the low-lying local minima have been also examined by the coupled-cluster method with single and double substitutions and perturbational estimate of triple excitations, CCSD(T). The ground state of CoO is a quartet ((4)Delta), in agreement with previous assignments, while the ground state of CoO- is a quintet ((5)Delta). The oxides CoO2 are more stable than the peroxides CO(O-2). The neutral oxide CoO2 in its ground state (6)A(1) is quasilinear; the monoanion in its (5)Delta(g) ground state is linear. Oxoperoxides OCo(O-2) are more stable than oxides CoO3 and superoxides OCoOO. Diperoxides are the stable structures for the uncharged CoO4. In general, the monoanions are more stable than the neutral clusters; however, electron attachment to peroxide destabilizes the O-O bond. The ground states of CoOn (n = 2-4) and the ground states of their anions [CoOn](-) are high-spin states-sextets for the neutral species and quintets for the anions. The thermodynamic stability of different structures was examined for possible fragmentation paths. The CoOn clusters and their monoanions dissociate preferably with the release of a dioxygen molecule.