  Gravitational radiation tends to drive gravity modes in rotating neutron
stars unstable. For an inviscid star, the instability sets in when the rotation
frequency is about 0.7 times the corresponding mode frequency of the
nonrotating star. Neutron stars with spin frequencies $\go 100$ Hz are
susceptible to this instability, with growth time of order years. However, it
is likely that viscous dissipation suppresses the instability except for a
narrow range of temperatures around $10^9$ K. We also show that the viscosity
driven instability of g-modes is absent.
