  We study accelerating cosmological solutions of a general class of non-linear
gravities which depend on Gauss-Bonnet and other higher derivative invariants.
To achieve this goal a local formulation with auxiliary scalars for arbitrary
higher-derivative non-local gravity is developed. It is demonstrated that
non-local Gauss-Bonnet gravity can be reduced, in the local formulation, to a
model of string-inspired scalar-Gauss-Bonnet gravity. A natural unification, in
the theory here developed, of the early-time inflation epoch with a late-time
acceleration stage can also be realized.
