Almost degenerate neutrinos with maximal mixing

We point out that if the observed deficit of solar and atmospheric neutrinos is to be understood as a consequence of oscillations between different neutrino flavors, the simplest way to reconcile it with the mixed dark matter picture of the universe and a possible sub-electron volt upper limit on the νe Majorana mass is to have a scenario of three light almost degenerate Majorana neutrinos (νe, νμ and ντ) with maximal CP-violating mixing among all three of them. We discuss theoretical scenarios which may lead to such a mass and mixing pattern. We also discuss a scenario where two of the three degenerate neutrinos are maximally mixed.