  We systematically investigate the complete class of vacuum solutions in the
Einstein-Gauss-Bonnet gravity theory which belong to the Kundt family of
non-expanding, shear-free and twist-free geometries (without gyratonic matter
terms) in any dimension. The field equations are explicitly derived and
simplified, and their solutions classified into three distinct subfamilies.
Algebraic structures of the Weyl and Ricci curvature tensors are determined.
The corresponding curvature scalars directly enter the invariant form of
equation of geodesic deviation, enabling us to understand the specific local
physical properties of the gravitational field constrained by the EGB theory.
We also present and analyze several interesting explicit classes of such vacuum
solutions, namely the Ricci type III spacetimes, all geometries with
constant-curvature transverse space, and the whole pp-wave class admitting a
covariantly constant null vector field. These exact Kundt EGB gravitational
waves exhibit new features which are not possible in Einstein's general
relativity.
