  We study a model of scalar field with a general non-minimal kinetic coupling
to itself and to the curvature, and additional coupling to the Gauss Bonnet
4-dimensional invariant. The model presents rich cosmological dynamics and some
of its solutions are analyzed. A variety of scalar fields and potentials giving
rise to power-law expansion have been found. The dynamical equation of state is
studied for two cases, with and without free kinetic term . In both cases
phenomenologically acceptable solutions have been found. Some solutions
describe essentially dark energy behavior, and and some solutions contain the
decelerated and accelerated phases.
