  Magnetohydrodynamic (MHD) instabilities can play an important role in the
structure and dynamics of the pulsar magnetosphere. We consider the
instabilitycaused by differential rotation that is suggested by many
theoretical models. Stability is considered by means of a linear analysis
within the frane of the force-free MHD. We argue that differentially rotating
magnetospheres are unstable for any particular geometry of the magnetic field
and rotation law. The characteristic growth time of instability is of the order
of the rotation period. The instability can lead to fluctuations of the
emission and enhancement of diffusion in the magnetosphere.
