  Neutrinos and antineutrinos of all three flavours are emitted during the post
bounce phase of a core collapse supernova with $\numu/\nutau (\anumu/\anutau)$
having average energies more than that of $\nue(\anue)$. They can be detected
by the new earth bound detector like SNO and Super-Kamiokande which are
sensitive to neutrinos of all three flavours. In this letter we consider the
effect of flavour oscillations on the neutrino flux and their expected number
of events at the detector. We do a three-generation analysis and for the mass
and mixing schemes we first consider the threefold maximal mixing model
consistent with the solar and the atmospheric neutrino data and next a scenario
with one $\Delta m^2 \sim 10^{-11} eV^2$ (solar range) and the other $\Delta
m^2 \sim 10^{-18} eV^2$, for which the oscillation length is of the order of
the supernova distance. In both these scenarios there are no matter effects in
the resultant neutrino spectrum and one is concerned with vacuum oscillations.
We find that though neutrino oscillations result in a depletion in the number
of $\nue$ and $\anue$ coming from the supernova, the actual signals at the
detectors are appreciable enhanced.
