It is shown that there exists an on-shell light cone gauge where half of th
e fermionic components of the super vector potential vanish, so that part o
f the superspace flatness conditions becomes linear. After reduction to (1
+ 1) space-time dimensions, the general solution of this subset of equation
s is derived, The remaining non-linear equations are written in a form whic
h is analogous to Yang equations, albeit with superderivatives involving si
xteen fermionic coordinates. It is shown that this non-linear part may, nev
ertheless, be solved by methods similar to powerful techniques previously d
eveloped for the (purely bosonic) self-dual Yang Mills equations in four di
mensions. (C) 1999 Elsevier Science B.V, All rights reserved.