The motion of a moored, or positioned, vessel under the influence of waves can be decomposed into a large-amplitude, slowly varying part and a small-amplitude, fast varying part. A consistent theory can be formulated, therefore, based on a multiple time scale expansion, together with an amplitude expansion of the general governing equations. The existing theory of ship motions remains unchanged within the present approach, while the equations of drift motion can be obtained separately from the fast dynamics, in a straightforward manner. It is shown that if the slow motion flow is modeled as inviscid and irrotational, its potential is of first order and satisfies linear boundary conditions. Also, the second-order force calculation is not influenced by the slow motions. The rolling motion of a moored vessel is studied as an example of the concepts introduced.