  In this paper, we first investigate the thermal stability of black holes in
conformal Weyl gravity with a comparison with the Schwarzschild black holes.
Then, we consider a minimally coupled massive scalar perturbation and calculate
the quasinormal modes in asymptotically dS spacetime by employing the sixth
order WKB approximation and asymptotic iteration method. The deviations from
those of the Schwarzschild-dS solutions are obtained and the possibility of the
presence of quasi-resonance modes for Weyl black hole solutions is
investigated. Finally, we consider a massless scalar perturbation in the
background of asymptotically AdS solutions and calculate the quasinormal modes
by using the pseudospectral method. The effects of the free parameter of the
theory on the quasinormal modes are studied and deviations from those of the
Schwarzschild-AdS black holes are investigated. The imaginary part of
quasinormal frequencies in AdS spacetime is the time scale of a thermal state
(in the conformal field theory) to approach thermal equilibrium.
