Structures of oxygen adsorbed on InN (1 0 (1) over bar 0) and (1 1 (2) over bar 0) surfaces are systematically investigated by first-principle calculations. Oxygen atoms may adsorb on the surface or substitute surface N atoms and act as a potential source of compensation for the p-type behavior on the InN (1 0 (1) over bar 0) surface. An InN (1 1 (2) over bar 0) surface structure covered by a 1/2 monolayer of oxygen is the most energetically favorable, which is qualitatively consistent with the experimental observations. (C) 2011 Elsevier B.V. All rights reserved.