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Here we shall show that there is no other instability for theEinstein-Gauss-Bonnet-anti-de Sitter (AdS) black holes, than the eikonal oneand consider the features of the quasinormal spectrum in the stability sectorin detail. The obtained quasinormal spectrum consists from the two essentiallydifferent types of modes: perturbative and non-perturbative in the Gauss-Bonnetcoupling $\alpha$. The sound and hydrodynamic modes of the perturbative branchcan be expressed through their Schwazrschild-AdS limits by adding a linear in$\alpha$ correction to the damping rates: $\omega \approx Re(\omega_{SAdS}) -Im(\omega_{SAdS}) (1 - \alpha \cdot ((D+1) (D-4) /2 R^2)) i$, where $R$ is theAdS radius. The non-perturbative branch of modes consists of purely imaginarymodes, whose damping rates unboundedly increase when $\alpha$ goes to zero.When the black hole radius is much larger than the anti-de Sitter radius $R$,the regime of the black hole with planar horizon (black brane) is reproduced.If the Gauss-Bonnet coupling $\alpha$ (or used in holography $\lambda_{GB}$) isnot small enough, then the black holes and branes suffer from the instability,so that the holographic interpretation of perturbation of such black holesbecomes questionable, as, for example, the claimed viscosity bound violation inthe higher derivative gravity. For example, $D=5$ black brane is unstable at$|\lambda_{GB}|>1/8$ and has anomalously large relaxation time when approachingthe threshold of instability.

Quasinormal modes of Gauss-Bonnet-AdS black holes: towards holographic description of finite coupling