  The dynamics of a binary system with two spinning components on an eccentric
orbit is studied, with the inclusion of the spin-spin interaction terms
appearing at the second post-Newtonian order. A generalized true anomaly
parametrization properly describes the radial component of the motion. The
average over one radial period of the magnitude of the orbital angular momentum
$\bar{L}$ is found to have no nonradiative secular change. All spin-spin terms
in the secular radiative loss of the energy and magnitude of orbital angular
momentum are given in terms of $\bar{L}$ and other constants of the motion.
Among them, self-interaction spin effects are found, representing the second
post-Newtonian correction to the 3/2 post-Newtonian order Lense-Thirring
approximation.
