  We develop a first-order approximation method for the influence of spin on
the motion of extended spinning test masses in a gravitational field. This
approach is illustrated for approximately circular equatorial motion in the
exterior Kerr spacetime. In this case, the analytic results for the first-order
approximation are compared to the numerical integration of the exact system and
the limitations of the first-order results are pointed out. Furthermore, we
employ our analytic results to illustrate the gravitomagnetic clock effect for
spinning particles.
