  A convenient formalism for averaging the losses produced by gravitational
radiation backreaction over one orbital period was developed in an earlier
paper. In the present paper we generalize this formalism to include the case of
a closed system composed from two bodies of comparable masses, one of them
having the spin S.
  We employ the equations of motion given by Barker and O'Connell, where terms
up to linear order in the spin (the spin-orbit interaction terms) are kept. To
obtain the radiative losses up to terms linear in the spin, the equations of
motion are taken to the same order. Then the magnitude L of the angular
momentum L, the angle kappa subtended by S and L and the energy E are
conserved. The analysis of the radial motion leads to a new parametrization of
the orbit.
  From the instantaneous gravitational radiation losses computed by Kidder the
leading terms and the spin-orbit terms are taken. Following Apostolatos,
Cutler, Sussman and Thorne, the evolution of the vectors S and L in the
momentary plane spanned by these vectors is separated from the evolution of the
plane in space. The radiation-induced change in the spin is smaller than the
leading-order spin terms in the momentary angular momentum loss. This enables
us to compute the averaged losses in the constants of motion E, L and L_S=L cos
kappa. In the latter, the radiative spin loss terms average to zero. An
alternative description using the orbital elements a,e and kappa is given.
  The finite mass effects contribute terms, comparable in magnitude, to the
basic, test-particle spin terms in the averaged losses.
