First-principles calculations based on density-functional theory (DFT) in the pseudopotential (PP) method have been performed for aluminum oxynitride with the spinel-type structure (gamma -alon). The calculations show that the face-centered sublattice of the anions is distorted, even for the hypothetical "ideal" gamma -alon spinel Al3O3N. Among the different proposed structure models, the model with vacancies on the Al sites (the so-called "constant anion model") is preferred, whereas a model with interstitial anions (the so-called "constant cation model") is unlikely. These results are in good agreement with the experimental results. The aluminum vacancies reside at the octahedral sites. The calculations also show that, in the structure of the gamma -alons, the O/N atoms are partially ordered. The space group Fd (3) over barm, which has been widely accepted for all gamma -alons, represents only the statistically averaged results that are obtained with diffraction techniques.