  We find the complex structure on the dual of a complex target space. For
$N=(2,2)$ systems, we prove that the space orthogonal to the kernel of the
commutator of the left and right complex structures is {\em always} integrable,
and hence the kernel is parametrized by chiral and twisted chiral superfield
coordinates. We then analyze the particular case of $SU(2)\times SU(2)$, and
are led to a new $N=2$ superspace formulation of the $SU(2)\times U(1)$
WZW-model.
