  Quasinormal modes of rapidly rotating black holes are crucial in
understanding the ringdown phase after a merger. While for Kerr black holes
these modes have been known for a long time, their calculation has remained a
challenge in alternative theories of gravity. We obtain the spectrum of
quasinormal modes of rapidly rotating black holes in
Einstein-Gauss-Bonnet-dilaton theory without resorting to perturbation theory
in the coupling constant. Our approach is based on a spectral decomposition of
the linear perturbations of the metric and the scalar field. The quasinormal
modes approach smoothly the slow rotation and weak coupling limits known from
perturbative studies.
