  We study the linear perturbations about a nonrotating black hole solution of
Horndeski's theory, using a systematic approach that extracts the asymptotic
behaviour of perturbations (at spatial infinity and near the horizon) directly
from the first-order radial differential system governing these perturbations
instead of finding Schr\"odinger-like equations for their dynamics. We
illustrate this method in the case of a specific black hole solution. The
knowledge of the asymptotic behaviours of the perturbations paves the way for a
numerical computation of the quasinormal modes. Finally, the asymptotic form of
the modes also signals some pathologies in the scalar sector of the solution
considered here.
