  For all $m \in \mathbb N - \{0\}$, we prove the existence of a one
dimensional family of genus $m$, constant mean curvature (equal to 1) surfaces
which are complete, immersed in $\mathbb R^3$ and have two Delaunay ends
asymptotic to nodo\"{\i}dal ends. Moreover, these surfaces are invariant under
the group of isometries of $\mathbb R^3$ leaving a horizontal regular polygon
with $m+1$ sides fixed.
