  The modified gravity with F(R,G) Lagrangian, G is the Gauss-Bonnet invariant,
is considered. It is shown that the phantom-divide-line crossing and the
deceleration to acceleration transition generally occur in these models. Our
results coincide with the known results of f(R)-gravity and f(G)-gravity
models. The contribution of quantum effects to these transitions is calculated,
and it is shown that in some special cases where there are no transitions in
classical level, quantum contributions can induce transitions. The quantum
effects are described via the account of conformal anomaly.
