  We present models that can reconcile the solar and atmospheric neutrino data
with the existence of a hot dark matter component in the universe. This dark
matter is a quasi-Dirac neutrino whose mass $m_{DM}$ arises at the one-loop
level. The solar neutrino deficit is explained via nonadiabatic conversions of
electron neutrino to a sterile neutrino and the atmospheric neutrino data via
maximal muon neutrino to tau neutrino oscillations generated by higher order
loop diagrams. For $m_{DM} \sim 30$ eV the radiative neutrino decay can lead to
photons that can ionize interstellar hydrogen. In one of the models one can
have observable $\nu_e$ to $\nu_\tau$ oscillation rates, with no appreciable
muon neutrino oscillations at accelerator experiments. In addition, there can
be observable rates for tau number violating processes such as $\tau \to 3e$
and $\tau \to e + \gamma$. In the other model one can have sizeable $\nu_e$ to
$\nu_\mu$ oscillation rates, as well as sizeable rates for muon number
violating processes such as $\mu \to e + \gamma$, $\mu \to e + majoron$ and
$\mu \to 3e$.
