The biocompatibility of NiTi shape memory alloys (SMA) has made possible applications in self-expandable cardio-vascular stents, stone extraction baskets, catheter guide wires and other invasive and minimally invasive biomedical devices. The NiTi intermetallic alloy spontaneously forms a thin passive layer of TiO(2), which provides its biocompatibility. The oxide layer is thought to form as the Ti in the alloy surface reacts with oxygen, resulting in a depletion of Ti in the subsurface region - experimental evidence indicates formation of a Ni-rich layer below the oxide film. In this paper, we study the initial stages of oxide growth on the (110) surface of the NiTi alloy to understand the formation of alloy/oxide interface. We initially adsorb atomic and molecular oxygen on the (110) surface and then successively add O(2) molecules, up to 2 monolayer of O(2). Oxygen adsorption always results in a large energy gain. With atomic oxygen, Ti is pulled out of the surface layer leaving behind a Ni-rich subsurface region. Molecular O(2), on the other hand adsorbs dissociatively and pulls a Ti atom farther out of the surface layer. The addition of further O(2) up to 1 monolayer is also dissociative and results in complete removal of Ti from the initial surface layer. When further O(2) is added up to 2 monolayer, Ti is pulled even further out of the surface and a single thin layer of composition O-Ti-O is formed. The electronic structure shows that the metallic character of the alloy is unaffected by interaction with oxygen and formation of the oxide layer, consistent with the oxide layer being a passivant.