The water uptake of different aqueous salt solutions in different Nafion membranes, and the salt transport through those membranes under the driving force of a concentration gradient, have been studied. These experiments have been performed by using the following salts: lithium chloride, sodium chloride, potassium chloride and cesium chloride. Different homogeneous Nafion membranes, NF111, NF112, NF115 and NF117, have been used in this work, with the aim of studying the membrane thickness influence. It has been observed that the membrane water uptake increases with the membrane thickness and decreases with the size of the cation. The integral permeability coefficient has been determined from the time evolution of the salt concentration in the dilute solution. The results show that the integral permeability coefficient decreases with the membrane thickness. In general, the influence of the type of electrolyte on the integral permeability coefficient is not significant for the membranes with larger thickness (that is, NF115 and NF117). Average apparent cation transport number has been determined for the same salt solutions, and from that membrane apparent permselectivity has been estimated. In general, in membranes with large thickness, the average apparent cation transport number increases with the cation size. Finally, from fluxes and membrane potentials membrane negative ionic permeabilities have been determined finding also that they decrease with membrane thickness. Salt diffusion coefficient has been also determined from membrane negative ionic diffusion coefficient.