  We construct sequences of rapidly rotating neutron stars in dilatonic
Einstein-Gauss-Bonnet theory, employing two equations of state for the nuclear
matter. We analyze the dependence of the physical properties of these neutron
stars on the Gauss-Bonnet coupling strength. For a given equation of state we
determine the physically relevant domain of rapidly rotating neutron stars,
which is delimited by the set of neutron stars rotating at the Kepler limit,
the set of neutron stars along the secular instability line, and the set of
static neutron stars. As compared to Einstein gravity, the presence of the
Gauss-Bonnet term decreases this domain, leading to lower values for the
maximum mass as well as to smaller central densities. The quadrupole moment is
decreased by the Gauss-Bonnet term for rapidly rotating neutron stars, while it
is increased for slowly rotating neutron stars. The universal relation between
the quadrupole moment and the moment of inertia found in General Relativity
appears to extend to dilatonic Einstein-Gauss-Bonnet theory with very little
dependence on the coupling strength of the Gauss-Bonnet term. The neutron stars
carry a small dilaton charge.
