  Material accreted onto a neutron star can stably burn in steady state only
when the accretion rate is high (typically super-Eddington) or if a large flux
from the neutron star crust permeates the outer atmosphere. For such situations
we have analyzed the stability of nonradial oscillations, finding one unstable
mode for pure helium accretion. This is a shallow surface wave which resides in
the helium atmosphere above the heavier ashes of the ocean. It is excited by
the increase in the nuclear reaction rate during the oscillations, and it grows
on the timescale of a second. For a slowly rotating star, this mode has a
frequency of approximately 20-30 Hz (for l=1), and we calculate the full
spectrum that a rapidly rotating (>>30 Hz) neutron star would support. The
short period X-ray binary 4U 1820--30 is accreting helium rich material and is
the system most likely to show this unstable mode,especially when it is not
exhibiting X-ray bursts. Our discovery of an unstable mode in a thermally
stable atmosphere shows that nonradial perturbations have a different stability
criterion than the spherically symmetric thermal perturbations that generate
type I X-ray bursts.
