This thesis describes the measurement of xenon diffusion coefficients in porous media via Pulsed Field Gradient (PFG) NMR spectroscopy. The thesis includes the characterization of a phase seperated polymer blend (PP/EPDM) in comparison to the pure components, the characterization of a number of commercially available semi-crystalline polymers and the characterization of a new microporous solid catalyst (silconimidonitride) with three different pore sizes by the diffusional behaviour of xenon in these materials. In addition to that a new theory is described which correlates the chemical shift of 129Xe NMR adsorption resonances with the corresponding xenon diffusion coefficients.