The self-diffusion coefficients of monovalent (Na+, K+, Cs', and Ag+) and divalent (Ca2+, Sr2+, Ba2+, and Zn2+) cations in Nafion-117 have been measured using the '"nonstationary radiotracer diffusion method" for the first time. This method is based on the analysis of absorption/desorption of radiotracer ions in the membrane sample as a function of time using an analytical solution of Fick's second law. It has been found to be simple and faster than that of the commonly used "radiotracer permeation method". An attempt has been made to interpret the self-diffusion data based on the free-volume theory. The self-diffusion coefficients for monovalent and divalent ions, normalized with respect to their aqueous diffusion coefficients, correlate well with the polymer volume fractions. However, separate trends are observed for monovalent and divalent ions. The factors that lead to higher self-diffusion coefficients of the counterions in the membrane appear to lower their selectivity coefficients.