  In the presence of a strong magnetic field and under conditions as realized
in the crust and the superfluid core of neutron stars the Hall--drift dominates
the field evolution. We show by a linear analysis that for a sufficiently
strong large--scale background field depending at least quadratically on
position in a plane conducting slab an instability occurs which rapidly
generates small--scale fields. Their growth rates depend on the choice of the
boundary conditions, increase with the background field strength and may reach
$10^3$ times the ohmic decay rate. The effect of that instability on the
rotational and thermal evolution of neutron stars is discussed.
