The linear hydrodynamic stability of proto-neutron stars (PNSs) is consider
ed, taking into account dissipative processes such as neutrino transport an
d viscosity. We obtain the general instability criteria, which differ essen
tially from the well-known Ledoux criterion used in previous studies. We ap
ply the criteria to evolutive models of PNSs that, in general, can be subje
ct to the various known regimes such as neutron fingers and convective inst
abilities. Our results indicate that the fingers instability arises in a mo
re extended region of the stellar volume and lasts a longer time than expec
ted.