  We report on a search for electro-magnetic and/or hadronic showers (cascades)
induced by high energy neutrinos in the data collected with the AMANDA II
detector during the year 2000. The observed event rates are consistent with the
expectations for atmospheric neutrinos and muons. We place upper limits on a
diffuse flux of extraterrestrial electron, tau and muon neutrinos. A flux of
neutrinos with a spectrum $\Phi \propto E^{-2}$ which consists of an equal mix
of all flavors, is limited to $E^2 \Phi(E)=8.6 x 10^{-7} GeV/(cm^{2} s sr)$ at
a 90% confidence level for a neutrino energy range 50 TeV to 5 PeV. We present
bounds for specific extraterrestrial neutrino flux predictions. Several of
these models are ruled out.
