  The equations governing the motion of a three-dimensional liquid drop moving
freely in an unbounded liquid reservoir under the influence of a gravitational
force are investigated. Provided the (constant) densities in the two liquids
are sufficiently close, existence of a steady-state solution is shown. The
proof is based on a suitable linearization of the equations. A setting of
function spaces is introduced in which the corresponding linear operator acts
as a homeomorphism.
