  Stability criteria of nearly extreme black holes in the perturbations level
is one of the interesting issues in gravitational systems. Considering the
nearly extreme conformal-de Sitter black holes, in this paper, we obtain an
exact relation for the quasinormal modes of scalar perturbations. As for
stability criteria, we find a lower bound on the event horizon radius which is
corresponding to an upper bound on the value of the quasinormal frequencies. In
addition, we show that the asymptotic behavior of quasinormal modes gives
highly damped modes which is important due to possible connection between their
real part and the Barbero-Immirzi parameter. We also obtain the Lyapunov
exponent and the angular velocity of unstable circular null geodesics. Finally,
we examine the validity of the relation between calculated quasinormal modes
and unstable circular null geodesics.
