The see-saw mechanism for neutrino masses based on the Grand Unificati
on leads to the mass of the heaviest neutrino (= nu(tau)) in the range
(2 - 3) . 10(-3) eV and hence to a solution of the solar neutrino pro
blem through the nu(e) --> nu(tau) conversion. We suggest the existenc
e of a light singlet fermion S which mixes predominantly with muon neu
trino through the mixing mass m(mu s) similar to O(1) eV. The introduc
tion of such a singlet allows one (i) to solve the atmospheric neutrin
o problem via the nu(mu) <-> S oscillations, (ii) to explain the LSND
result and (iii) to get two component hot dark matter in the Universe.
The phenomenology of this scenario is considered and the origin of th
e singlet as well as of the scale m(mu s) is discussed. (C) 1998 Elsev
ier Science B.V. All rights reserved.