We give a new derivation of the quasinormal frequencies of
Schwarzschild black holes in d greater than or equal to 4 and
Reissner-Nordstrom black holes in d = 4, in the limit of infinite damping.
For Schwarzschild in d greater than or equal to 4 we find that the asymptotic real part
is THawkinglog(3) for scalar perturbations and for some gravitational perturbations; this confirms a
result previously obtained by other means in the case d = 4. For
Reissner-Nordstrom in d = 4 we find a specific generally aperiodic behavior
for the quasinormal frequencies, both for scalar perturbations and for
electromagnetic-gravitational perturbations. The formulae are obtained by
studying the monodromy of the perturbation analytically continued to the complex plane;
the analysis depends essentially on the behavior of the potential in the 'unphysical' region
near the black hole singularity.