  In this paper, we first construct two-dimensional periodic interface waves
with point vortex and capillary effect and then obtain the global structure of
the set of solutions. This is done using the local and global bifurcation
argument. Especially, we establish a global continuation theorem by using the
degree for $C^1$ Fredholm mappings. As far as we know, the global result is new
and general, which is promising to deal with other new phenomena in water
waves.
