  It is shown that the singular seesaw mechanism can simultaneously explain all
the existing data supporting nonzero neutrino masses and mixing. The three
mass-squared differences that are needed to accommodate the atmospheric
neutrino data (through $\nu_\mu - \nu_s$ oscillation), the solar neutrino data
via MSW mechanism (through $\nu_e - \nu_\tau$ oscillation), and the positive
result of $\nu_\mu - \nu_e$ oscillation from LSND can be generated by this
mechanism, whereas the vacuum oscillation solution to the solar neutrino
problem is disfavored. We find that the electron and tau neutrino masses are of
order $10^{-3}$ eV, and the muon neutrino and a sterile neutrino are almost
maximally mixed to give a mass of order 1 eV. Two heavy sterile neutrinos have
a mass of order 1 keV which can be obtained by the double seesaw mechanism with
an intermediate mass scale $\sim 10^5$ GeV. A possible origin of such a scale
is discussed.
