Spin-polarized density functional calculations are used to study the adsorption of O atoms and O-2 molecules on graphite and on a (8,0) single-walled carbon nanotube. An O atom is found to bind to graphite and to the outside and inside surfaces of the nanotube to give stable epoxide-like structures. Of these, the most stable is the epoxide on the outer surface of the nanotube, with a calculated adsorption energy of 44 kcal/mol. In the case of O-2, both physisorbed and chemisorbed species are identified. The O-2 molecule is predicted to only weakly physisorb (adsorption energy approximate to 0.9 kcal/mol) to the graphite and the (8,0) nanotube surfaces. However, these adsorption energies are expected to be underestimated due to inadequate treatment of the dispersion interactions. The chemisorbed species are metastable in the sense that they lie energetically above the isolated X (3)Sigma (+)(g) O-2 and graphite or nanotube systems. In the case of the outer wall of the nanotube, the chemisorbed species is predicted to lie only 10.2 kcal/mol above the reactants. The reaction of O-2 with the nanotube surface to give two epoxide groups is predicted to be slightly exothermic.