  We perform dimensional reductions of recently constructed self-dual $~N=2$~
{\it supersymmetric} Yang-Mills theory in $~2+2\-$dimensions into
two-dimensions. We show that the universal equations obtained in these
dimensional reductions can embed supersymmetric exactly soluble systems, such
as $~N=1$~ and $~N=2$~ supersymmetric Korteweg-de Vries equations, $~N=1$~
supersymmetric Liouville theory or supersymmetric Toda theory. This is the
first supporting evidence for the conjecture that the $~2+2\-$dimensional
self-dual {\it supersymmetric} Yang-Mills theory generates {\it supersymmetric}
soluble systems in lower-dimensions.
