  In the present paper we take a step towards the generalization of the
post-Newtonian formalism to tensor-multi-scalar theories. These are theories
where we have more than one scalar field being mediators of the gravitational
interaction in addition to the spacetime metric. They are very natural
extensions of Einstein's gravity allowing for the existence of new classes of
compact objects and offering interesting phenomenology reaching far beyond the
single scalar field theories. We calculate the expansion up to 2.5
post-Newtonian order in the near zone using the so-called direct integration of
the relaxed Einstein equations formalism and derive the equation of motion.
This work is the first step towards the calculation of gravitational waveforms
in tensor-multi-scalar theories.
