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Magnetohydrodynamic (MHD) instabilities can play an important role in thedynamics of the pulsar magnetosphere and can be responsible for the formationof various structures. We consider the instability caused by a gradient of themagnetic pressure which can occur in a non-neutral magnetospheric plasma. Wearguethat the pulsar magnetospheres are always unstable. The unstabledisturbances have a form of filaments directed along the magnetic field lineswith plasma motions being almost parallel (or anti-parallel) to the magneticfield. 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 beresponsible for fluctuations of plasma and the short-term variability of pulsaremission.

Formation of filament-like structures in the pulsar magnetosphere and the short-term variability of pulsar emission