  We derive the explicit analytic expression for the Stokes' drift in one
dimension in the presence of a dichotomic Markov forcing. For small amplitudes
of the forcing, the drift is enhanced, but the enhancement is reduced with
increasing frequency of the forcing. On the other hand, a reduction of the
drift or even a flux reversal can be induced at larger amplitudes, while the
flux is now found to be an increasing function of the perturbation frequency.
