Spin-orbit and spin-spin effects in the gravitational interaction are treated in a close analogy with the fine and hyperfine interactions in atoms. The proper definition of the center-of-mass coordinate is discussed. The technique developed is applied then to the gravitational radiation of compact binary stars. Our result for the spin-orbit correction differs from that obtained by other authors. New effects possible for the motion of a spinning particle in a gravitational field are pointed out. The corresponding corrections, nonlinear in spin, are in principle of the same order of magnitude as the ordinary spin-spin interaction. E-mail: firstname.lastname@example.org c flThe State Research Center of Russian Federation "Budker Institute of Nuclear Physics SB RAS" . 1. It is expected that in few years the gravitational radiation from coalescing binary stars will be observed by laser interferometer systems LIGO and VIRGO. Its successful detection depends crucially on the accurate theoret..