The double-scaling limit of the supereigenvalue model is performed in
the moment description. This description proves extremely useful for t
he identification of the multi-critical points in the space of bosonic
and fermionic coupling constants. An iterative procedure for the calc
ulation of higher-genus contributions to the free energy and to the mu
lti-loop correlators in the double-scaling limit is developed. We pres
ent the general structure of these quantities at genus g and give expl
icit results up to and including genus two.