A tetrahedral model is presented to explain the bonding properties of nonstoichiometric amorphous silicon oxynitride (a-SiOxNy) alloys, grown under highly nonequilibrium conditions, whose structures obey neither the random bonding model nor the random mixture model. Based on our approach, a numerical procedure is proposed to obtain the relative atomic percentages of each component structural phase from the deconvolution of the high-resolution x-ray photoelectron spectroscopy (XPS) spectra in the Si 2p3/2 region. The tetrahedral model is then used to study the bonding properties of a-SiOxNy films grown by electron-cyclotron resonance plasma-enhanced chemical-vapor deposition, having relatively low values of the O/Si atomic ratio (≤0.37) incorporated in their networks. The experimental results show that five tetrahedral phases (tetrahedrons Si–Si4, Si–Si2ON, Si–N4, Si–Si3O, and Si–O4) are present in a-SiOxNy films with low N/Si atomic ratios (≤0.93), while only three phases (Si–SiON2, Si–N4, and Si–O2N2) are present in samples with higher N/Si atomic ratios (≥1.12). The Si3N4 phase is the most important bonding unit and it is the only phase present in all our samples. These results are corroborated by survey scans and by comparison with the high-resolution XPS spectra in the N 1s region. They support the validity of the model proposed for a-SiOxNy alloys and the XPS analysis, correlated with growth conditions, presented in this work.