An algorithm is developed for computing the nth gravitational multipole moment of an asymptotically flat, empty, stationary axisymmetric space-time. The moments are expressed in terms of the expansion coefficients of the Ernst potential on the axis of symmetry. The values of the first ten multipole moments are given.

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The electromagnetic and gravitational multipole moments of stationary sources in general relativity are obtained in the conformal picture in terms of the expansion coefficients of the electrovacuum potentials on the axis of symmetry. Generic expressions for the values of the first five multipole moments are given, and the field of a pure pole-dipole source is investigated.

The secular evolution of a spinning, massive binary system in eccentric orbit is analyzed, expanding and generalizing our previous treatments of the Lense-Thirring motion and the one-spin limit. The spin-orbit and spin-spin effects up to the 3/2 post-Newtonian order are considered, both in the equations of motion and in the radiative losses. The description of the orbit in terms of the true anomaly parametrization provides a simple averaging technique, based on the residue theorem, over eccentric orbits. The evolution equations of the angle variables characterizing the relative orientation of the spin and orbital angular momenta reveal a speed-up effect due to the eccentricity. The dissipative evolution of the relevant dynamical and angular variables is presented in the form of a closed system of differential equations.

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