  It has recently been found that quasinormal modes of asymptotically anti-de
Sitter (AdS) black holes in theories with higher curvature corrections may help
to describe the regime of intermediate 't Hooft coupling in the dual field
theory. Here, we consider quasinormal modes of a scalar field in the background
of spherical Gauss--Bonnet--anti-de Sitter (AdS) black holes. In general, the
eigenvalues of wave equations are found here numerically, but at a fixed
Gauss-Bonnet constant $\alpha = R^2/2$ (where $R$ is the AdS radius), an exact
solution of the scalar field equation has been obtained. Remarkably, the purely
imaginary modes, which are usually appropriate only to some gravitational
perturbations, were found here even for a test scalar field. These purely
imaginary modes of the Einstein--Gauss--Bonnet theory do not have the
Einsteinian limits, because their damping rates grow, when $\alpha$ is
decreasing. Thus, these modes are nonperturbative in $\alpha$. The real
oscillation frequencies of the perturbative branch are linearly related to
their Schwarzschild-AdS limits $Re (\omega_{GB}) = Re (\omega_{SAdS}) (1+ K(D)
(\alpha/R^2))$, where $D$ is the number of spacetime dimensions. Comparison of
the analytical formula with the frequencies found by the shooting method allows
us to test the latter. In addition, we found exact solutions to the master
equations for gravitational perturbations at $\alpha=R^2/2$ and observed that
for the scalar type of gravitational perturbations an eikonal instability
develops.
