  In this paper, we extend the first-order post-Newtonian scheme in multiple
systems presented by Damour-Soffel-Xu to the second-order contribution to light
propagation without changing the virtueof the scheme on the linear partial
differential equations of the potential and vector potential. The spatial
components of the metric are extended to second order level both in a global
coordinates ($q_{ij}/ c^4$) and a local coordinates ($Q_{ab}/ c^4$). The
equations of $q_{ij}$ (or $Q_{ab}$) are obtained from the field equations.The
relationship between $q_{ij}$ and $Q_{ab}$ are presented in this paper also. In
special case of the solar system (isotropic condition is applied ($q_{ij} =
\delta_{ij} q $)), we obtain the solution of $q$. Finally, a further extension
of the second-order contributions in the parametrized post-Newtonian formalism
is discussed.
