  We compute the Nicolai map for the supersymmetric Yang-Mills theory, in the
light-cone gauge, to the second order in the coupling constant for all critical
dimensions (d=3,4,6,10). The process of integrating out unphysical degrees of
freedom in this gauge, produces a four fermion interaction term. We show that,
to the order investigated here, this term is harmless. We demonstrate the
existence of a particularly `simple' map in d=4 in the light-cone gauge and
address the issue of uniqueness in the context of the map. We also investigate
the map in the light-cone superspace in d=4.
