129Xe-NMR spectra of polyethylene samples showed inhomogeneously broadened lines at room-temp. Two-dimensional exchange expts. show that there is no exchange of Xe between various sites on a time scale of seconds. The line is attributed to Xe in the mobile amorphous regions of the polymer, whose resonance is broadened due to susceptibility variations induced by the distribution of cryst. lamellas. At temps. below the b-transition, a 2nd line is obsd. in the Xe spectrum, possibly related to a decreased mobility in some parts of the amorphous phase. Xe exchanged between void spaces in an amorphous polycarbonate on the NMR time scale.