Small-angle X-ray and neutron-scattering techniques have been used to probe the structure of swollen Nafion membranes in the range 10-10000 Angstrom. From analyzing the scattering data as a function of the polymer volume fraction and using a contrast variation method for the neutron experiments, we suggest a new structural model of Nafion in the hydrated state. It is based on the aggregation of the ionomer chains into elongated polymeric bundles with a diameter on the order of 40 Angstrom and a length larger than 1000 Angstrom, surrounded by the electrolyte solution.