We have studied the generation of interface states, for different injection current densities, during constant current Fowler-Nordheim tunnelling injection stress in oxynitride films grown on silicon by rapid thermal processing in dry oxygen and nitriding in ammonia. The increase of the interface state density at the midgap (DeltaD(itm)) is found to be a power function of the injected charge density (Q(inj)), for values of Q(inj) > 2 A cm(-2) and does not saturate until breakdown. The power coefficient is found to be approximately equal to 0.3 and is almost independent of the injection current density. An analysis of the data for oxide films obtained by others gives the same coefficient, The above result indicates that the mechanism of the degradation for the oxide films is the same as, or similar to, the oxynitride films. The extrapolated values of DeltaD(itm) for the instant just prior to the breakdown lie in the range from 5 x 10(11) eV(-1) cm(-2) to 5 x 10(12) eV(-1) cm(-2), independent of the injection current density.