When three Majorana neutrinos describe the solar and atmospheric neutrino d
ata via oscillations, a nonzero measurement of neutrinoless double beta (0
nu beta beta) decay can determine the sum of neutrino masses Sigma m(nu) if
the solar solution has small-angle mixing, and place a lower bound on Cm,
for large-angle solar mixing. If in addition a nonzero Gin, is deduced from
cosmology, the neutrino mass spectrum may be uniquely specified for some r
anges of neutrino parameters. For Sigma m(nu) > 0.75 eV, the small-angle so
lar solution is excluded by the current upper limit on neutrinoless double
beta decay. In models with maximal solar mixing the CP phases of the neutri
nos may be strongly constrained by stringent upper bounds on 0 nu beta beta
decay. (C) 1999 Published by Elsevier Science B.V. All rights reserved.