  There exists both theoretical and observational evidence that the magnetic
field decay in neutron stars may proceed in a pronounced non--linear way during
a certain episode of the neutron star's life. In the presence of a strong
magnetic field the Hall--drift dominates the field evolution in the crust
and/or the superfluid core of neutron stars. Analysing observations of $P$ and
$\dot{P}$ for sufficiently old isolated pulsars we gain strong hints for a
significantly non--linear magnetic field decay. Under certain conditions with
respect to the geometry and strength of a large--scale magnetic background
field an instability is shown to occur which rapidly raises small--scale
magnetic field modes. Their growth rates increase with the background field
strength and may reach $\sim 10^4$ times the ohmic decay rate. Consequences for
the rotational and thermal evolution as well as for the cracking of the crust
of neutron stars are discussed.
