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