We consider the influence of the Hall effect on the evolution of a str
ong magnetic field which can magnetize plasma. The Hall current couple
s various multipole field components and provides a possibility of an
energy exchange among modes. Due to this, the evolution of strong magn
etic fields is substantially more complicated than the ohmic decay of
weak magnetic fields. Non-linear effects can create a complex magnetic
configuration even from the simplest one corresponding originally to
the pure dipole field outside the star. The energy transfer among fiel
d components leads to a non-monotonic behaviour of individual modes. V
ariations of the large scale magnetic field are of the same origin as
the so called helicoidal oscillation of magnetized plasma. The period
of variations is determined by the time scale associated with the Hall
effect and may be sufficiently short for a strong magnetic field. The
non-linear phenomena may be important for the magnetic evolution of w
hite dwarfs and neutron stars.