A conducting liquid with a free surface is subjected to a vertical magnetic force due to imposed, horizontal, magnetic and current fields in the liquid. Because the current field is modified differently by differently oriented surface waves, the propagation of gravity waves becomes strongly anisotropic. The cases of shallow and deep fluid are explored. The group velocity shows features that are reminiscent of magnetoacoustic waves. The need for stability of the surface sets limits on the magnetic force which may be imposed. The feasibility of experiments is discussed and the effect of ohmic damping and surface tension is found to be relatively unimportant under suitably chosen conditions.