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This work describes proton transport in membranes cast from dimethyl sulfoxide solutions of polyelectrolytes obtained by polycondensation of 4,4′-diaminodiphenyl ether (ODA) and 4,4′-diaminodiphenyl ether-2,2′-disulfonic acid (ODADS) with 1,4,5,8-naphthalenetetracarboxylic dianhydride (NTDA), the moles of sulfonated diamine per mole of unsulfonated one being roughly 3/1. Pulsed field gradient (PFG) NMR studies reveal two kinds of water: water located in the pores of the membranes appearing in the range 5 to 1 ppm and a minor amount of water associated with the imide groups, appearing at 1 ppm. The diffusion coefficient of 1H in the first type of water is about 2 orders of magnitude higher than that measured in the second type and in both cases the values of this parameter severely decrease as the water content of the membranes decreases. The diffusion coefficients of bare protons, hydronium ions and water in the membranes were calculated using molecular dynamics techniques. For membranes with low water content, the diffusion coefficient of 1H is very close to the diffusion coefficients of water and hydronium ions obtained by simulation. At high concentrations the simulated values are higher than D(1H). The simulated values obtained for the diffusion coefficients of hydronium ion and water for membranes equilibrated with water are fairly close to those estimated, respectively, from proton conductivity and osmotic measurements. This work suggests that the study of cation-exchange membranes in the acidic form using NMR, conductivity, and molecular dynamics simulation techniques provides useful information on how structure and water content affect transport processes in membranes.