Nucleic acids promote amyloid formation in diseases including Alzheimer's and Creutzfeldt-Jakob disease. However, it remains unclear whether the close interactions between amyloid and nucleic acid allow nucleic acid secondary structure to play a role in modulating amyloid structure and function. Here we have used a simplified system of short basic peptides with alternating hydrophobic and hydrophilic amino acid residues to study nucleic acid - amyloid interactions. Employing biophysical techniques including X-ray fibre diffraction, circular dichroism spectroscopy and electron microscopy we show that the polymerized charges of nucleic acids concentrate and enhance the formation of amyloid from short basic peptides, many of which would not otherwise form fibres. In turn, the amyloid component binds nucleic acids and promotes their hybridisation at concentrations below their solution K(d), as shown by time-resolved FRET studies. The self-reinforcing interactions between peptides and nucleic acids lead to the formation of amyloid nucleic acid (ANA) fibres whose properties are distinct from their component polymers. In addition to their importance in disease and potential in engineering, ANA fibres formed from prebiotically-produced peptides and nucleic acids may have played a role in early evolution, constituting the first entities subject to Darwinian evolution.