  We consider the gravitational sector of the superstring effective action with
axion-matter couplings. The field equations are developed in the post-Newtonian
scheme and approximate solutions for a spinning point mass and a cosmic string
are presented. Furthermore, assuming vanishing axion mass and vanishing
potential for the dilaton, we consider the gravitational radiation in the
leading $O(\alpha'^0)$ order. We find that the total luminosity of a radiative
source has monopole and dipole components besides the standard quadrupole one.
These components may possibly be checked in binary systems.
