  The conditions for the existence and stability of cosmological power-law
scaling solutions are established when the Einstein-Hilbert action is modified
by the inclusion of a function of the Gauss-Bonnet curvature invariant. The
general form of the action that leads to such solutions is determined for the
case where the universe is sourced by a barotropic perfect fluid. It is shown
by employing an equivalence between the Gauss-Bonnet action and a scalar-tensor
theory of gravity that the cosmological field equations can be written as a
plane autonomous system. It is found that stable scaling solutions exist when
the parameters of the model take appropriate values.
