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 mDM 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 mDM∼30 eV the radiative neutrino decay can lead to photons that can ionize interstellar hydrogen. In one of the models one can have observable νe to ντ 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 τ→3e and τ→e+γ. In the other model one can have sizeable νe to νμ oscillation rates, as well as sizeable rates for muon number violating processes such as μ→e+γ, μ→e+majoron and μ→3e.