  A measurement of the big bang relic neutrinos would open a new window to the
early universe. We review various possibilities to detect this cosmic neutrino
background and substantiate the assertion that -- apart from the rather
indirect evidence to be gained from cosmology and large-scale structure
formation -- the annihilation of ultrahigh energy cosmic neutrinos with relic
anti-neutrinos (or vice versa) on the Z-resonance is a unique process having
sensititivy to the relic neutrinos, if a sufficient flux at E^res_{nu_i} =
M_Z^2/(2 m_{nu_i}) = 4 x 10^{22} eV (0.1 eV/m_{nu_i}) exists. The associated
absorption dips in the ultrahigh energy cosmic neutrino spectrum may be
searched for at forthcoming neutrino and air shower detectors. The associated
protons and photons may have been seen already in form of the cosmic ray events
above the Greisen-Zatsepin-Kuzmin cutoff.
