Silicon oxynitride thin films were sputter deposited by the reactive gas pulsing process. Pure silicon target was sputtered in Ar, N2 and O2 mixture atmosphere. Oxygen gas was periodically and solely introduced using exponential signals. In order to vary the injected O2 quantity in the deposition chamber during one pulse at constant injection time (TON), the tau mounting time τmou of the exponential signals was systematically changed for each deposition. Taking into account the real-time measurements of the discharge voltage and the I(O*)/I(Ar*) emission lines ratio, it is shown that the oscillations of the discharge voltage during the TON and TOFF times (injection of O2 stopped) are attributed to the preferential adsorption of the oxygen compared to that of the nitrogen. The sputtering mode alternates from a fully nitrided mode (TOFF time) to a mixed mode (nitrided and oxidized mode) during the TON time. For the highest injected O2 quantities, the mixed mode tends toward a fully oxidized mode due to an increase of the trapped oxygen on the target. The oxygen (nitrogen) concentration in the SiOxNy films similarly (inversely) varies as the oxygen is trapped. Moreover, measurements of the contamination speed of the Si target surface are connected to different behaviors of the process. At low injected O2 quantities, the nitrided mode predominates over the oxidized one during the TON time. It leads to the formation of Si3N4-yOy-like films. Inversely, the mixed mode takes place for high injected O2 quantities and the oxidized mode prevails against the nitrided one producing SiO2-xNx-like films.