  In a recent paper [1], motivated by forthcoming space experiments involving
propagation of light in the Solar System, we have proposed an extention of the
IAU metric equations at the c-4 level in General Relativity. However,
scalar-tensor theories may induce corrections numerically comparable to the c-4
general relativistic terms. Accordingly, one first proposes in this paper an
extension of [1] to the scalar-tensor case. The case of a hierarchized system
(such as the Solar system) is emphasized. In this case, the relevant metric
solution is proposed. Then, the geodesic solution relevant for propagation of
light in the inner solar system at the millimetric level is given in explicit
form.
