We use molecular dynamics simulations to investigate the structure of the hydrated Na-Nafion membranes. The membrane is '' prepared '' by starting with the Nafion chains placed on a cylinder having the water inside it. Minimizing the energy of the system leads to a filamentary hydrophilic domain whose structure depends on the degree of hydration. At 5 wt % water the system does not have enough water molecules to solvate all the ions that could be formed by the dissociation of the -SO3Na groups. As a result, the -SO3Na groups aggregate with the water to form very small droplets that do not join into a continuous phase. The size of the droplets is between 5 and 8 angstrom. As the amount of water present in the membrane is increased, the membrane swells, and SO3Na has an increasing tendency to dissociate into ions. Furthermore, a transition to a percolating hydrophilic network is observed. In the percolating structure, the water forms irregular curvilinear channels branching in all directions. The typical dimension of the cross section of these channels is about 10-20 angstrom. Calculated neutron scatterine, from the simulated system is in qualitative agreement with experiment. In all simulations, the pendant sulfonated perfluorovinyl side chains of the Nafion hug the walls of the hydrophilic channel, while the sulfonate groups point toward the center of the hydrophilic phase. The expulsion of the side chains from the hydrophilic domain is favored because it allows better interaction between the water molecules. We have also examined the probability of finding water molecules around the Na+ and the -SO3- ions as well as the probability of finding other water molecules next to a given water molecule. These probabilities are much broader than those found in bulk water or for one ion in bulk water (calculated with the potentials used in the present simulation). This is due to the highly inhomogeneous nature of the material contained in the small hydrophilic pores.