Xenon self-diffusion coeffs. of com. available org. polymers have been detd. by application of pulsed field gradient (PFG) NMR spectroscopy. Xenon diffusion in elastomeric EPDM was found to be about 20 times faster than in the more rigid isotactic polypropylene (PP). In a polymer blend of both materials consisting of 80% PP and 20% EPDM both diffusion coeffs. are in the same range and between the values of the pure materials. As SEM pictures show, this incompatible blend consists of small EPDM domains (1-3 mm) within the PP matrix. The root mean square displacement of xenon within the time interval of the PFG NMR expt. is greater than the domain sizes of EPDM. These results also evidence that xenon in this blend is mainly absorbed in EPDM domains and in the PP matrix near the PP/EPDM interface.