The pressure-dependent permeation of heavy noble gases through oriented polypropylene (OPP) is explained with a phenomenological model based on the hopping-like migration of particles over a network of trapping sites with random site energies. The main mechanism behind the pressure dependence of the permeation is related to a decrease in the average activation energy of diffusion upon the gas sorption. This decrease is achieved because of a saturation of the deep traps, which reduces the mass transport to a network of shallow traps. In this way, fast-diffusion channels with lower activation energy are created. The model is suitable for the description of the transient permeation of a gas through a polymer, as illustrated for the permeation of noble gases through an OPP membrane. (C) 2003 Wiley Periodicals, Inc.