The well known Damour - Soffel - Xu (DSX) formalism of relativistic celestial mechanics and astronomical reference systems is restricted to the first post - Newtonian (1PN) approximation of Einstein ’ s theory of gravity. The key features of the DSX - formalism are: the use of N+ 1 different coordinate systems for the description of the gravitational N body problem and a special canonical way of writing the metric tensor in these N+1coordinate systems; introducing the potentials (w, W) and vector potentials (w i ,W a ) to describe the metric tensor in global coordinates (small symbols) and in the local coordinate systems where the metric potentials satisfy linear equations and separating W and W a into internal and external parts in every N local coordinate systems. The internal part is determined by local gravitational sources (Blanchet - Damour (B - D) multipole moments) and the external part can be determined by matching the metric tensors in the global and the local system. It is the purpose of this work to extend the DS X formalism to include also certain terms of second post - Newtonian (2PN) order. Since one main field of application will be high - precision astrometry only the spatial part of the metric tensor will be modified to correctly describe the propagation of light - rays to 2PN order, considering also terms of order c - 6 . In this way new potentials (q ij , Q ab ) appear in the global and local metric tensors. These new potentials are related with the DSX metric potentials and the energy - momentum tensor and also satisfy linear equations. H ere it should be emphasized that the introduction of q ij and Q ab does not influence the relations and equations for the metric potentials, i.e., they do not destroy the spirit of the DSX formalism in our extension. As well as in the DSX formalism Q ab can be separated into an internal part Q +ab and an external part, ab . The Q +ab - terms in a local system will be related with the B - D mass - multipole moments of the body under consideration and a set of new multipole moments related with the shear - stresses inside the body. The relation between ij and ab can be also deduced from a matching condition and the spatial harmonic gauge condition. One rather complex situation is that the external super - potential term appears in the inhomogeneous term of the linear relation between ij and ab . The transformation rules for the new potentials from the local to the global frame will be derived. In this way the modified global metric tensor will be obtained. Even for a system of mass monopoles the global spatial metric will contain additional terms to the Einstein - Infeld - Hoffmann metric (from which the EIH - equations can be derived), the ab terms. Consequences of these ab terms for light - propagation are studied by analytical estimations and numerical integration of the light - ray (null geodesics) equation. Although there are many papers devoted to the problem of light propagation to 2PN order, but none of them has discussed the problem in N+1 coordinate systems. Our work is the first complete discussion on the problem of the light propagation in the 2 PN order within the frame of N +1 coordinate systems.