  We investigate the possibility of detecting cosmic ultra-high energy
tau-neutrinos by means of a process involving a double extensive air shower,
the so-called Double-Bang Phenomenon. In this process a primary tau-neutrino
interacts with an atmospheric quark creating a first hadronic shower and a
tau-lepton, which subsequently decays creating a second cascade. The number of
these events strongly depends on the flux of tau-neutrinos arriving at the
Earth's atmosphere and can be used to test some theoretical models related to
the production of ultra-high energy tau-neutrinos. We estimate the potential of
the fluorescence detector of the Pierre Auger Observatory to observe
Double-Bang events. We conclude that for tau-neutrinos with energies ranging
from ~ 0.1 EeV to ~ 10 EeV the number of detected events vary from hundreds in
a year to only few events in hundreds of years.
