  We consider a multi-fluid system with several free interfaces. For this
system we prove existence of three-dimensional steady gravity-capillary waves
with non-zero vorticity. We obtain non-zero vorticity by prescribing the
relative velocity fields to be Beltrami fields, for which the vorticity and
velocity are parallel. The main result is a multi-parameter bifurcation result
for small amplitude waves given in two variants: a first theorem guaranteeing
existence under some general parameter assumptions; and a second specific but
less exhaustive theorem, for which the assumptions may be explicitly verified,
yielding the existence of both in-phase and off-phase motions in the different
layers. The proof relies on an implicit function theorem corresponding to
multi-parameter bifurcation. This theorem is presented in an appendix as an
abstract result that can be applied directly to other problems.
