Saveliev and the author recently showed that there exists an on-shell light
-cone gauge where the nonlinear part of the field equations reduces to a (s
uper) version of the Yang equations that can De solved using methods inspir
ed by those previously developed for the self-dual Yang-Mills equations in
four dimensions. Here, the analogy between these latter theories and the pr
esent ones is extended by writing a set of super linear partial differentia
l equations that have consistency conditions derivable from the supersymmet
ric Yang-Mills equations in 10 dimensions and are analogues of the Belavin-
Zakharov Lax pair. In the simplest example of the two-pole ansatz, the same
solution-generating techniques work as in the derivation of the multi-inst
anton solutions in the late 1970s. The present Lax representation, however,
is only a consequence of (instead of being equivalent to) the field equati
ons, in contrast to the Belavin-Zakharov Lax pair.