As part of a program to quantize superstrings in AdS(5) X S-5 in a light-co
ne gauge we find the explicit form of the corresponding Green-Schwarz actio
n in the fermionic light-cone kappa -symmetry gauge. The resulting action c
ontains terms quadratic and quartic in fermions. In the nat space limit it
reduces to the standard light-cone GS action, while for alpha'-->0 it has t
he correct AdS(5) X S-5 light-cone superparticle limit. We discuss fixing t
he bosonic light-cone gauge and a reformulation of the action in terms of 2
D Dirac spinors.