The nature of the stability of incommensurate long-period structures in alloys of the system Cu-Au is investigated on the basis of first-principles calculations of the electronic structure. It is shown that many structural properties of such formations can be explained only if the latter are treated as superstructures with respect to ordinary superstructures (L12 or L10): the electron spectrum of the superstructure and not that of the initial disordered alloy must serve as the initial spectrum. The observed dependence of the long period N on the degree η ?of the “short” long-range order is explained. The reasons why two-dimensional long-period superstructures from in the alloy Au3Cu are found. Arguments supporting the fact that among quasicrystalline substances long-period superstructures fall between incommensurate systems and quasicrystals are presented.