Titanium Oxynitride (TiOxNy) thin films are fabricated using reactive magnetron sputtering. The mechanism of their growth formation is explained and their optical properties are presented. The films grown when the level of residual Oxygen in the background vacuum was between 5E-9Torr to 20E-9Torr exhibit double Epsilon-Near-Zero (2-ENZ) behaviour with ENZ1 and ENZ2 wavelengths tunable in the 700-850 nm and in the 1100-1350 nm spectral ranges, respectively. Samples fabricated when the level of residual Oxygen in the background vacuum was above 2E-8Torr exhibit non-metallic behaviour, while the layers deposited when the level of residual Oxygen in the background vacuum was below 5E-9Torr, show metallic behaviour with a single ENZ value. The double ENZ phenomenon is related to the level of residual Oxygen in the background vacuum and is attributed to the mixture of TiN and TiOxNy/TiOx phases in the films. Varying the partial pressure of nitrogen during the deposition can further control the amount of TiN, TiOx and TiOxNy compounds in the films and, therefore, tune the screened plasma wavelength. A good approximation of the ellipsometric behaviour is achieved with Maxwell-Garnett theory for a composite film formed by a mixture of TiO2 and TiN phases suggesting that double ENZ TiOxNy films are formed by inclusions of TiN within a TiO2 matrix. These oxynitride compounds could be considered as new materials exhibiting double ENZ in the visible and near-IR spectral ranges.