for any flavour. If one of the neutrinos had a mass near this bound it would provide a significant fraction of the cosmic dark matter. Theories of cosmological structure formation disfavour ``hot dark matter'' (e.g. neutrinos). However, ``cold dark matter'' (e.g. neutralinos) overproduce structure on small scales, a problem that can be patched up in a ``mixed dark matter'' scenario with . Even a ``sub-critical'' neutrino mass is cosmologically interesting! Besides relying on the standard big-bang picture, Eq. () depends on the assumption that neutrinos do not decay fast on cosmological time scales. The dominant standard-model decays of mixed neutrinos are or which are far too slow to invalidate Eq. (). In addition, radiative decays have been constrained from the absence of anomalous cosmic photon backgrounds in various energy bands. The experimental mass limit exceeds 2me so that is possible, and could be fast enough to invalidate Eq. (). However, rays for the inner Bremsstrahlung process have not been observed by the SMM or COMPTEL satellites from SN 1987A, providing very restrictive limits on this process. One infers that all three sequential neutrinos must obey Eq. () unless they decay fast into ``invisible'' channels by non-standard couplings. Turning this around, experimental searches for neutrinos with masses exceeding Eq. () are tantamount to searching for novel neutrino couplings beyond the standard model. The signal duration of SN 1987A yields a limit on dispersion effects. In particular
somewhat less restrictive than the corresponding laboratory limits from tritium decay. The best direct mass limits could be obtained from a future galactic SN if the neutrino signal is measured in a detector like Superkamiokande in conjunction with the proposed Supernova Burst Observatory (SNBO). Optimistically, one may be able to achieve a sensitivity down to the 10 eV range even for and .