Mobility is a socioeconomic reality that increases every year and it should be safe, economic and reasonably clean. Little energy needs to be expended to overcome potential energy changes, but a great deal is lost through friction and low-efficiency energy conversion. Vehicles can run either by connecting them to a continuous supply of energy or by storing energy on board. Hydrogen would be ideal as a synthetic fuel because it is lightweight, highly abundant and its oxidation product (water) is environmentally benign, but storage remains a problem. The clean way to produce hydrogen from water is to use sunlight in combination with photovoltaic cells and water electrolysis, although other forms of primary energy and other water-splitting processes are generally used. The chemical energy per mass of hydrogen (142 MJ/kg) is at least three times larger than that of other chemical fuels. Hydrogen adsorbs at solid surfaces depending on the applied pressure and the temperature. The variation of attractive surface forces as a function of distance from the surface decides whether van der Waals-type weak physisorption of molecular hydrogen occurs, or whether dissociation and chemisorption of atomic hydrogen takes place. For storage purposes in mobile applications, the adsorption of hydrogen has been mainly studied on carbon species, but light and reasonably cheap materials of high surface area should prove to be attractive as well. In this work nanocomposites with sulfonated polyetherimide and faujasite-type zeolite doped with aluminium were prepared using different amounts of nanoparticles. Their morphology and hydrogen storage capacity were evaluated. Taking previous results, it is considered scientifically interesting and challenging to continue research on the interaction of hydrogen with different and well-characterized polymer-based nanocomposites.