  We find the quasinormal modes of the charged scalar and Dirac fields in the
background of the rotating charged black holes, described by the Kerr-Newman-de
Sitter solution. The dependence of the quasinormal spectrum upon the black hole
parameters mass M, angular momentum a, charge Q, as well as on values of the
\Lambda-term and field charge q is investigated. Special attention is given to
the near extremal limit of the black hole charge. In particular, we find that
for both scalar and Dirac fields, charged perturbations decay quicker for q>0
and slower for q<0 for values of black holes charge Q less than than some
threshold value, which is close to the extremal value of charge and depend on
parameters of the black holes.
