  We study gravitational perturbations of the Kerr-AdS_5 x S^5 spacetime with
equal angular momenta. In this spacetime, we found the two kinds of classical
instabilities, superradiant and Gregory-Laflamme instabilities. The
superradiant instability is caused by the wave amplification via superradiance,
and by wave reflection due to the potential barrier of the AdS spacetime. The
Gregory-Laflamme instability appears in Kaluza-Klein modes of the internal
space S^5 and breaks the symmetry SO(6). Taken into account these
instabilities, the phase structure of Kerr-AdS_5 x S^5 spacetime is revealed.
The implication for the AdS/CFT correspondence is also discussed.
