The phenomenon of adsorption and desorption of xenon in an inorg. aluminum/zircon oxide fiber, in silica gel and in an org. polymer blend is compared by 129Xe 2-dimensional-exchange NMR expts. A fast chem. exchange between adsorbed, liq. and free xenon gas occurs in the case of the alumina/zirconia fiber. In contrast to this, for the polymer blend, exchange between different adsorption sites in the blend is obsd., but no exchange between adsorbed xenon and xenon gas. Hardly any exchange of xenon between adsorbed and free gas occurs in silica gel even at larger time scales. The inorg. fiber has an open pore structure, in contrast to the examd. copolymer.