The self-diffusion coefficients of Li-7(+) in a suspension of sulfonated polystyrene latex particles is determined by pulsed-field-gradient, spin-echo NMR over a wide range of electrolyte concentrations. The self-diffusion coefficient of the Li+ counterion in the suspension without electrolyte is significantly less than that found in a solution of LiClO4 at the same bulk concentration. This suggests that a large fraction of the Li+ counterions are electrostatically bound to the large latex particles. The effective charge on the particles is inferred from this measurement. The self-diffusion coefficient of Li+ increases upon the addition of NaClO4 to the deionized suspension. Measuring selectively the dependence of Li+ diffusion on the amount of added electrolyte characterizes the ion-exchange behavior of the latex suspension. The self-diffusion coefficients determined by NMR agree with prediction of the nonlinear Poisson-Boltzmann equation and gradient-diffusion coefficients of hydrogen counterion determined in the same latex by steady-state voltammetry.