The growth kinetics of silicon oxynitride (SiO_x:N) thin films grown on silicon in N₂O ambient in a conventional oven, at high pressures and temperatures has been investigated. Starting from the Deal and Grove (Deal and Grove 1965 J. Appl. Phys. 36 3770) model for silicon oxidation in O₂, applied to this problem, we have found that the activation energy for the diffusion coefficient of the nitridating species (NO) is 2.54 eV. Similarly, the activation energy for the O₂ diffusion coefficient through the oxynitride layer was also determined to be 3.67 eV. From these results we conclude that the NO molecules diffuse faster than O₂ in the silicon oxynitride films, which explains why in spite of a high proportion of O₂ being present in the gas phase, the oxynitridation is limited by the kinetics of the NO molecules, causing a growth rate much less than for the oxidation of silicon in O₂.