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The radiative evolution of the relative orientations of the spin and orbitalangular momentum vectors ${\bf S}_{{\bf 1}}, {\bf S}_{{\bf 2}}$ and ${\bf L}$,characterizing a binary system on eccentric orbit is studied up to the secondpost-Newtonian order. As an intermediate result, all Burke-Thorne typeinstantaneous radiative changes in the spins are shown to average out over aradial period. It is proved that spin-orbit and spin-spin terms contribute tothe radiative angular evolution equations, while Newtonian, first and secondpost-Newtonian terms together with the leading order tail terms do not. Incomplement to the spin-orbit contribution, given earlier, the spin-spincontribution is computed and split into two-body and self-interaction parts.The latter provide the second post-Newtonian order corrections to the 3/2 orderLense-Thirring description.Comment: 8 pages, to appear in Phys. Rev.

Second post-Newtonian radiative evolution of the relative orientations of angular momenta in spinning compact binaries