We present time-dependent xenon diffusion measurements over a wide range of diffusion times in three different silicon imidonitrides. a new class of microporous catalysts, by PFG NMR spectroscopy. Our exptl. data show that for short diffusion times D a sharp decrease of the diffusion coeff. D with increasing D occurs, while in the long-time regime D approaches a const. value. We correlate the differences in the diffusional behavior with the pore structure of the material. Addnl., we found that for these materials there is a linear correlation between the chem. shift of the 129Xe resonances and the corresponding long-time diffusion coeff.