  Poisson-Lie T-duality in N=2 superconformal WZNW models on the real Lie
groups is considered. It is shown that Poisson-Lie T-duality is governed by the
complexifications of the corresponding real groups endowed with
Semenov-Tian-Shansky symplectic forms, i.e. Heisenberg doubles. Complex
Heisenberg doubles are used to define on the group manifolds of the N=2
superconformal WZNW models the natural actions of the isotropic complex
subgroups forming the doubles. It is proved that with respect to these actions
N=2 superconformal WZNW models admit Poisson-Lie symmetries. Poisson-Lie
T-duality transformation maps each model into itself but acts nontrivialy on
the space of classical solutions.
