The coupled radiation-diffraction problem due to a floating body with slow (time-dependent) rotation about the vertical axis in incoming waves is studied by means of potential theory. The water depth may be finite. First, the radiation problem is described. It is shown how the various components of the velocity potential may be obtained by means of integral equations. The first-order forces in the coupled radiation-diffraction problem are then considered. Generalized Haskind relations for the exciting forces and generalized Timman–Newman relations for the added mass and damping forces are deduced for bodies of arbitrary shape with vertical walls at the water line. The equation of motion is obtained, and the frequencies of the linear body responses superposed on the slow rotation are identified. Formulae for the wave-drift damping coefficients in the yaw mode of motion are derived in explicit form, and the energy equation is discussed. Computations illustrating the various aspects of the method are performed for two ships. The wave-drift damping moment is found to become positive in the present examples. When the rotation axis is moved far away from the body, the slow motion becomes effectively unidirectional, and results of the translational case are recovered.