  In this work, we present the quasinormal modes of a fermionic field in the
background of Gauss-Bonnet-AdS black holes. We find exact solutions for $D=5$
at the fixed value $\alpha=R^2/2$ of the Gauss--Bonnet coupling constant, with
$R$ denoting the AdS radius, and we find numerical solutions for some range of
values of the coupling constant $\alpha$ and $D=5, 6$. Mainly, we find two
branches of quasinormal frequencies, a branch perturbative in the Gauss-Bonnet
coupling constant $\alpha$, and another branch nonperturbative in $\alpha$. The
phenomena of nonperturbative modes, which seem to be quite general in theories
with higher curvature corrections, have been obtained in the spectrum of
gravitational field perturbations and scalar field perturbations in previous
works. We show that it also arises for fermionic field perturbations and
therefore seems to be independent of the spin of the field under consideration.
However, in contrast to gravitational and scalar field perturbations, where the
nonperturbative modes are purely imaginary, we find that for fermionic field
perturbations the nonperturbative modes acquire a real part. We find that the
imaginary part of the quasinormal frequencies is always negative in both
branches; therefore, the spherical Gauss-Bonnet-AdS black holes are stable
against fermionic field perturbations.
