  The loop equation for the complex one-matrix model with a multi-cut structure
is derived and solved in the planar limit. An iterative scheme for higher genus
contributions to the free energy and the multi-loop correlators is presented
for the two-cut model, where explicit results are given up to and including
genus two. The double-scaling limit is analyzed and the relation to the one-cut
solution of the hermitian and complex one-matrix model is discussed.
