  In the context of the supersymmetric flipped $SU(5)\otimes U(1)$ GUT model,
we have studied in detail the neutrino mass spectrum, obtaining an approximate
formula for the corresponding effective three-generation mass matrix. It is
found that at least two neutrinos are expected to have extremely small masses
of no particular interest. The third neutrino, on the other hand, may
eventually get a mass of order $10^{-3}$ eV, of relevance for the solution of
the solar neutrino problem with the MSW mechanism, as a consequence of
vacuum-expectation-values at the GUT mass scale for some of the scalar partners
of the right-handed neutrinos.
