  In this paper we look at the gravitational spin--spin interaction between
macroscopic astronomical bodies. In particular, we calculate their
post--Newtonian orbital effects of order $\mathcal{O}(c^{-2})$ on the
trajectory of a spinning particle with proper angular momentum ${\bf s}$ moving
in the external gravitomagnetic field generated by a central spinning mass with
proper angular momentum ${\bf J}$. It turns out that, at order $\mathcal{O}(e)$
in the orbiter's eccentricity, the eccentricity the pericenter and the mean
anomaly rates of the moving particle are affected by long--term harmonic
effects. If, on one hand, they are undetectable in the Solar System, on the
other, maybe that in an astrophysical context like that of the binary
millisecond pulsars there will be some hopes of measuring them in the future.
