  The temperature of the cosmic microwave background increases with redshift;
at sufficiently high redshift it becomes possible for ultrahigh-energy photons
and electrons to produce muons and pions through interactions with background
photons. At the same time, energy losses due to interactions with radio
background and intergalactic magnetic fields are negligible. The energetic
muons and pions decay, yielding a flux of ``signature'' neutrinos with energies
$E_\nu \sim 10^{17}$eV. Detection of these neutrinos can help understand the
origin of ultrahigh-energy cosmic rays.
