  The quasinormal resonant modes of massless neutral fields in near-extremal
Kerr-Newman-de Sitter black-hole spacetimes are calculated in the eikonal
regime. It is explicitly proved that, in the angular momentum regime ${\bar a}>
\sqrt{{{1-2{\bar\Lambda}}\over{4+{\bar\Lambda}/3}}}$, the black-hole spacetimes
are characterized by slowly decaying resonant modes which are described by the
compact formula $\Im\omega(n)=\kappa_+\cdot(n+{1\over2})$ [here the physical
parameters $\{{\bar a},\kappa_+,{\bar\Lambda},n\}$ are respectively the
dimensionless angular momentum of the black hole, its characteristic surface
gravity, the dimensionless cosmological constant of the spacetime, and the
integer resonance parameter]. Our results support the validity of the Penrose
strong cosmic censorship conjecture in these black-hole spacetimes.
