Atomic oxygen chemisorption has been studied for the fourfold hollow site of the Ni(100) surface and for the threefold hollow site of the Ni(111) surface. To model the Ni(100) surface, 10 different clusters in the range Ni5 to Ni41 were used, and for the Ni(111) surface, 11 different clusters in the range Ni13 to Ni43 were used. A detailed analysis of the orbital occupations of the cluster with and without oxygen for the different clusters shows that there are three different possible bonding mechanisms. In two of these, the basic feature is that a1 electrons of the cluster are kicked out by the oxygen 2p(z) orbital and moved to holes in the 2p(x,y) orbitals. A picture where the oxygen electrons fit into the electronic structure of the cluster is emphasized. The third mechanism, which is applicable for only one cluster, can be described as the formation of two covalent bonds of E symmetry. The final best estimate of the oxygen chemisorption energy for the Ni(100) surface is about 130 kcal/mol, and for the Ni(111) surface, about 115 kcal/mol. In particular for the Ni(111) surface, an excited oxygen state with radical character is identified, which might be a catalytically important species. The excitation energy to reach this state should be on the order of 10 kcal/mol for the Ni(111) surface.