The structure and chemical composition of low-index surfaces of NiAl are investigated by grand canonical Monte Carlo simulations. Atomic interactions in NiAl are modeled by an embedded-atom potential fit to experimental and first-principles data. The simulations are performed at the temperature of 1200 K for the stoichiometric and two Ni-rich bulk compositions. For the (110) surface, the top surface layer is slightly enriched in Ni relative to the bulk whereas deeper layers are slightly depleted in Ni, so that the overall Gibbsian surface adsorption is almost zero. For the (100) and (111) surface orientations, the Al termination is structurally stable but contains a certain percentage of Ni atoms, depending on the bulk composition. The Al (111) termination also develops a large amount of vacancies and adatoms. The Ni terminations of the (100) and (111) surfaces are both unstable and transform to the respective Al terminations. This transformation can take place by two different mechanisms. One mechanism is the development of a terrace surface structure with areas of Al termination separated by stoichiometric (110) facets. An alternative mechanism, observed only for the (100) surface, is the injection of an antiphase boundary into the bulk with a simultaneous switch of the surface termination to Al. It is demonstrated that this mechanism cannot work for the (111) surface.