  In this talk the Schwarz hypothesis that the duality symmetries should be
pieces of the hidden gauge symmetry in a string theory is discussed. Using
auxiliary linear system special dual transformations for $N=4$ SYM generalizing
the Schwarz dual transformations for a principal chiral model are constructed.
These transformations are related with a continuous group of hidden symmetry of
a new model involving more fields as compare with $N=4$ SYM. We conjecture that
the $Z_{2}$ discrete subgroup of this hidden symmetry group has a stable set of
N=4 YM fields and transforms a self-dual configuration to an anti-self-dual and
via versa.
