  Quasinormal modes of scalar, electromagnetic, and gravitational fields in the
extreme Schwarzschild-de Sitter background are known to be expressed in
analytic form as eigenvalues of the P\"oschl-Teller wavelike equation. We show
that perturbations of fermionic fields (given by Dirac and Rarita-Schwinger
equations) do not lead to the P\"oschl-Teller effective potential.
Nevertheless, using the Frobenius method we find quasinormal modes analytically
in this case as well. We write down the analytical formula for quasinormal
frequencies of the near-extreme Schwarzschild-de Sitter black holes, which is
valid for both bosonic and fermionic fields. We further extend the analysis to
the case of charged rotating black holes and find a general analytical formula
for quasinormal modes of the fields of various spin for the near extreme
Kerr-Newman-de Sitter spacetime.
