  We take as a starting point the Gelmini -- Roncadelli model enlarged by a
term with explicit lepton number violation in the Higgs potential and add a
neutrino singlet field coupled via a scalar doublet to the usual leptons. This
scenario allows us to take into account all three present indications in favour
of neutrino oscillations provided by the solar, atmospheric and LSND neutrino
oscillation experiments. Furthermore, it suggests a model which reproduces
naturally one of the two 4-neutrino mass spectra favoured by the data. In this
model the solar neutrino problem is solved by large mixing MSW \nu_e\to\nu_\tau
transitions and the atmospheric neutrino problem by transitions of \nu_\mu into
a sterile neutrino.
