The invention relates to a process for the controlled growth of nanotubes or nanofibers on a substrate, characterized in that it furthermore comprises the production, on the substrate (11), of a bi-layer structure composed of a layer of catalyst material (71), for catalyzing the growth of nanotubes or nanofibers, and a layer of associated material, said associated material being such that it forms a noncatalytic alloy with the catalyst material at high temperature.The invention also relates to a process for fabricating a field-emission cathode using the above nanotube or nanofiber fabrication process.These processes allow very precise positioning of the catalyst spots from which the nanotubes and nanofibers can be grown and allow the fabrication of cathodes for which the nanotubes or nanofibers are self-aligned with the aperture in the extraction grid.Applications: electron tubes, nanolithography.