Spectra of xenon-129 sorbed into two high permeability polymers are reported. The polymers are the copolymer of tetrafluoroethylene and 2,2-bis(trifluoromethyl)-4,5-difluoro-1,3-dioxole as well as poly(1-trimethylsilyl-1-propyne). At room temperature, the xenon-129 shifts are smaller than in conventional glassy polymers. The smaller xenon-129 shift indicates the presence of larger sorption sites in high permeability polymers relative to conventional polymers. The temperature dependence of solubility in these polymers is drastically different from the behavior in conventional polymers. There is a rapid exponential increase in solubility in high permeability polymers as temperature decreases corresponding to a large negative enthalpy change on sorption and it is this increase in solubility which leads to a large increase in shift with decreasing temperature. Pulse field gradient (PFG) determinations of the self-diffusion constant are made for xenon, propane, pentane and a decafluoropentane in the copolymer. Rapid diffusion is observed as well as a dependence of the apparent diffusion constant on the time scale of the PFG experiment. The translational mobility of smaller simpler moieties depends less on the time scale or equivalently, the length scale of observation in the PFG NMR experiment. For larger, more complex species, the interconnectedness of high free volume domains plays a role in reducing the apparent diffusion constant as the time of measurement increases.