Two general models with hierarchical and almost degenerate neutrino masses,
which are able to explain the solar and atmospheric anomalies are investig
ated. We show how neutrinoless double beta decay experiments discern Dirac
and Majorana natures of neutrinos. The strongest result is, that almost deg
enerate neutrinos with masses above 0.22 eV combined with the SMA MSW must
be Dirac particles. In the general case, the same bound is true for specifi
c parity assignments. In the near future (GENIUS experiment), one of the hi
erarchical schemes, and the VO mechanism for almost degenerate neutrinos an
d specific mixing matrix elements and parity assignments will be tested. (C
) 1999 Elsevier Science B.V. All rights reserved.