  Magnetohydrodynamic (MHD) instabilities can play an important role in the
dynamics of the pulsar magnetosphere and can be responsible for the formation
of various structures. We consider the instability caused by a gradient of the
magnetic pressure which can occur in a non-neutral magnetospheric plasma. We
arguethat the pulsar magnetospheres are always unstable. The unstable
disturbances have a form of filaments directed along the magnetic field lines
with plasma motions being almost parallel (or anti-parallel) to the magnetic
field. The growth rate of instability is high and can reach a fraction of $ck$,
where $k$ is the wavevector of unstable disturbances. The instability can be
responsible for fluctuations of plasma and the short-term variability of pulsar
emission.
