  Using post-Newtonian equations of motion for fluid bodies that include
radiation-reaction terms at 2.5 and 3.5 post-Newtonian (PN) order O[(v/c)^5]
and O[(v/c)^7] beyond Newtonian order), we derive the equations of motion for
binary systems with spinning bodies, including spin-spin effects. In particular
we determine the effects of radiation-reaction coupled to spin-spin effects on
the two-body equations of motion, and on the evolution of the spins. We find
that radiation damping causes a 3.5PN order, spin-spin induced precession of
the individual spins. This contrasts with the case of spin-orbit coupling,
where there is no effect on the spins at 3.5PN order. Employing the equations
of motion and of spin precession, we verify that the loss of total energy and
total angular momentum induced by spin-spin effects precisely balances the
radiative flux of those quantities calculated by Kidder et al.
