  We investigate the evolution of a scalar field propagating in
Reissner--Nordstr\"{o}m Anti--de Sitter spacetime. Due to the characteristic of
spacetime geometry, the radiative tails associated with a massless scalar field
propagation have an oscillatory exponential decay. The object--picture of the
quasinormal ringing has also been obtained. For small charges, the approach to
thermal equilibrium is faster for larger charges. However, after the black hole
charge reaches a critical value, we get the opposite behavior for the imaginary
frequencies of the quasinormal modes. Some possible explanations concerning the
wiggle of the imaginary frequencies have been given. The picture of the
quasinormal modes depending on the multipole index has also been illustrated.
