We demonstrate the formation of supra-molecular peptide nanofibers that display dynamic instability; i.e., they are formed by competing assembly and disassembly reactions, where assembly is favored away from equilibrium. The systems are based on competitive catalytic transacylation and hydrolysis, producing a self-assembling aromatic peptide amphiphile from amino acid precursors that temporarily exceeds the critical gelation concentration, until the competing hydrolytic reaction takes over. Analysis by atomic force microscopy shows consecutive nanofiber formation and shortening. The process results in macroscopically observable temporary hydrogelation, which may be repeated upon refueling the system with further addition of the chemically activated amino acid precursor. Nonequilibrium nanostructures open up opportunities for mimicry of the behavior of dynamic gels found in natural systems and provide components for future adaptive nanotechnologies.