  We study two-dimensional periodic capillary-gravity water waves propagating
at the free surface of water in a flow with arbitrary, prescribed vorticity
over a flat bed. Using conformal mappings and a new Babenko-type reformulation
of Bernoulli's equation, the problem is equivalently cast into the form
"identity plus compact", which is amenable to Rabinowitz' global bifurcation
theorem, while no restrictions on the geometry of the surface profile and no
assumptions regarding the absence of stagnation points in the flow have to be
made. Within the scope of this new formulation, local and global solution
curves, bifurcating from laminar flows with a flat surface, are constructed.
