An integral form of the discrete superloop equations for the supereige
nvalue model of Alvarez-Gaume, Itoyama, Manes and Zadra is given. By a
change of variables from coupling constants to moments we find a comp
act form of the planar solution for general potentials. In this framew
ork an iterative scheme for the calculation of higher genera contribut
ions to the free energy and the multi-loop correlators is developed. W
e present explicit results for genus one.