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In the present thesis, the leading-order post-Newtonian spin-orbit and spin (1)-spin(2) radiation-reaction Hamiltonians are calculated.We utilize the canonicalformalism of Arnowitt, Deser, and Misner (ADM), which has shown to be valuable for this kind of calculation.The results are valid for arbitrary many objects.The energy loss is then computed and compared to well-known results for theenergy flux as a check.