The invention relates to a process for the growth of nanotubes or nanofibers on a substrate comprising at least an upper layer made of a first material, wherein: the formation, on the surface of the upper layer, of a barrier layer made of an alloy of the first material and of a second material, said alloy being stable at a first temperature; the formation of spots of catalyst that are made of the second material, on the surface of the alloy layer; and the growth of nanotubes or nanofibers at a second temperature below said first temperature. The alloy layer allows effective growth of nanotubes/nanofibers from catalyst spots on the surface of said alloy layer. This is because the alloy layer constitutes a diffusion barrier preventing the catalyst from diffusing into the growth substrate, which barrier is stable at the catalytic nanotube/nanofiber growth temperature.