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 neu
trino singlet field that is coupled via a scalar doublet to the usual lepto
ns. This scenario allows us to take into account all three present indicati
ons in favor of neutrino oscillations provided by the solar, atmospheric, a
nd LSND neutrino oscillation experiments. Furthermore, it suggests a model
which reproduces naturally one of the two 4-neutrino mass spectra favored b
y the data. In this model, the solar neutrino problem is solved by large mi
xing MSW nu(e) --> nu(tau) transitions, and the atmospheric neutrino proble
m by transitions of nu(mu) into a sterile neutrino.