A new experimental approach for measuring diffusion coefficients of sorbed gas in polymers has been developed based on a combination of NMR spectroscopy and the use of polymer microspheres. The system chosen to demonstrate the technique is xenon gas sorbed into polystyrene beads of micron size. Pressures in the range of 10-15 atm are sealed in NMR tubes containing a gram or so of polymer. Chemical shift exchange of the xenon gas is easily monitored in either one or two dimensions through the xenon-129 resonances since well-separated signals are observed for the sorbed and free gas. To quantitatively determine diffusion coefficients, selective saturation of the gas phase resonance is used to reduced that signal to zero. Then the decay of the sorbed signal is monitored as a function of saturation time to determine the rate of diffusion of gas out of the polymer microsphere. Diffusion in this case is simply described mathematically by diffusion out of a sphere. A model has been developed to take into account the effects of diffusion in combination with spin-lattice relaxation of the xenon-129 sorbed in the polymer. The diffusion coefficient of xenon in polystyrene at 25 degrees C is (1.9 +/- 0.4) x 10(-9) cm(2)/s. Measurements were made up to 115 degrees C and an apparent activation energy of 36 kJ/mol was found for diffusion in glassy polystyrene with a sharp increase in the diffusion coefficient when the glass transition region was reached.