  New methods are proposed with the goal to determine absolute neutrino masses
from the simultaneous observation of the bursts of neutrinos and gravitational
waves emitted during a stellar collapse. It is shown that the neutronization
electron neutrino flash and the maximum amplitude of the gravitational wave
signal are tightly synchronized with the bounce occuring at the end of the core
collapse on a timescale better than 1 ms. The existing underground neutrino
detectors (SuperKamiokande, SNO, ...) and the gravity wave antennas soon to
operate (LIGO, Virgo, ...) are well matched in their performance for detecting
galactic supernovae and for making use of the proposed approach. Several
methods are described, which apply to the different scenarios depending on
neutrino mixing. Given the present knowledge on neutrino oscillations, the
methods proposed are sensitive to a mass range where neutrinos would
essentially be mass-degenerate. The 95 % C.L. upper limit which can be achieved
varies from 0.75 eV/c2 for large electron neutrino survival probabilities to
1.1 eV/c2 when in practice all electron neutrinos convert into muon or tau
neutrinos. The sensitivity is nearly independent of the supernova distance.
