  We explore, mostly using data from solar neutrino experiments, the hypothesis
that the neutrino mass eigenstates are unstable. We find that, by combining
$^8$B solar neutrino data with those on $^7$Be and lower-energy solar
neutrinos, one obtains a mostly model-independent bound on both the $\nu_1$ and
$\nu_2$ lifetimes. We comment on whether a nonzero neutrino decay width can
improve the compatibility of the solar neutrino data with the massive neutrino
hypothesis.
