We report on the experimental observation of dual magnonic and phononic bandgaps in bi-component nanostructured crystals. The dispersion relations of linear periodic arrays of alternating Fe (or Ni) and Ni Fe nanostripes on a SiO /Si substrate, mapped by Brillouin spectroscopy, feature distinct bandgaps. Calculations of the magnon and phonon dispersions yield good agreement with experiments. No magnon-phonon interaction is detected for the modes observed, making the structures studied a potential platform for the separate and simultaneous processing of information carried by hypersonic magnons and phonons, with no undesirable cross-talk between them. © 2012 American Institute of Physics.