We consider the gravitational sector of the superstring effective acti
on with axion-matter couplings. The field equations are developed in t
he post-Newtonian scheme and approximate solutions for a spinning poin
t mass and a cosmic string are presented. Furthermore, assuming vanish
ing axion mass and vanishing potential for the dilaton, we consider th
e gravitational radiation in the leading O(alpha'0) order. We find tha
t the total luminosity of a radiative source has monopole and dipole c
omponents besides the standard quadrupole one. These components may po
ssibly be checked in binary systems.