  We consider the stability properties of the ocean of accreting magnetic
neutron stars. It turns out that the ocean is always unstable due to the
combined influence of the temperature and chemical composition gradients along
the surface and of the Hall effect. Both the oscillatory and non-oscillatory
modes can be unstable in accreting stars. The oscillatory instability grows on
a short timescale of the order os 0.1-10 s depending on the lengthscale of a
surface inhomogeneity and the wavelength of perturbations. The instability of
non-oscillatory modes is typically much slower and can develop on a timescale
of hours or days. Instability generates a weak turbulence that can be
responsible for mixing between the surface and deep ocean layers and for
spreading the accreted material over the stellar surface. Spectral features of
heavy elements can be detected in the atmospheres of accreting stars due to
mixing, and these features should be different in neutron stars with stable and
unstable burning. Motions caused by instability can also be the reason for slow
variations in the luminosity.
