  Top-down models of cosmic rays produce more neutrinos than photons and more
photons than protons. In these models, we reevaluate the fluxes of neutrinos
associated with the highest energy cosmic rays in light of mounting evidence
that they are protons and not gamma rays. While proton dominance at EeV
energies can possibly be achieved by efficient absorption of the dominant
high-energy photon flux on universal and galactic photon and magnetic
background fields, we show that the associated neutrino flux is inevitably
increased to a level where it should be within reach of operating experiments
such as AMANDA II, RICE and AGASA. In future neutrino telescopes, tens to a
hundred, rather than a few neutrinos per kilometer squared per year, may be
detected above 1 PeV.
