An emerging new direction of research focuses on developing "self-synthesizing materials", those supramolecular structures that can promote their own formation by accelerating the synthesis of building blocks and/or an entire assembly. It was postulated recently that practical design of such systems can benefit from the ability to control the assembly of amphiphilic molecules into nanostructures. We describe here the self-assembly pathway of short amphiphilic peptides into various forms of soluble β-sheet structures--β-plates, fibrils, and hollow nanotubes--and their consequent activity as autocatalysts for the synthesis of monomeric peptides from simpler building blocks. A detailed kinetic analysis of both the self-assembly and self-replication processes allows us to suggest a full model and simulate the replication process, revealing that only specific structures, primarily fibrils that are stable within the solution for a time shorter than a few hours, can be active as catalysts. Interestingly, we have found that such a process also induces fibril reproduction, in a mechanism very similar to the propagation of prion proteins by transmission of misfolded states.