We have measured the frequency‐dependent complex dielectric permittivity of silicon oxynitride films in the frequency range 10−4–107Hz for temperatures of 290–365 K. The dielectric permittivity displays a conductivity relaxation at low frequencies and gradually goes over to an almost frequency‐independent complex permittivity at high frequencies. The experimental data can be accounted for by assuming that the conductivity relaxation is superimposed on the frequency‐independent contribution to the permittivity. On that premise, the conductivity relaxation and the onset of dc conductivity are in good agreement with calculations by the continuous time random walk model employing a distribution of transition rates pertinent to a fractal time process.