  The general phenomena associated with sustained resonance are studied in this
paper in connection with relativistic binary pulsars. We represent such a
system by two point masses in a Keplerian binary system that evolves via
gravitational radiation damping as well as an external tidal perturbation. For
further simplification, we assume that the external tidal perturbation is
caused by a normally incident circularly polarized monochromatic gravitational
wave. In this case, the second-order partially averaged equations are studied
and a theorem of C. Robinson is employed to prove that for certain values of
the physical parameters resonance capture followed by sustained resonance is
possible in the averaged system. We conjecture that sustained resonance can
occur in the physical system when the perturbing influences nearly balance each
other.
