T-duality of axial and vector dyonic integrable models

A general construction of affine Non Abelian (NA) - Toda models in terms of axial and vector gauged two loop WZNW model is discussed. They represent {\it integrable perturbations} of the conformal $\sigma$-models (with tachyons included) describing (charged) black hole type string backgrounds. We study the {\it off-critical} T-duality between certain families of axial and vector type of integrable models for the case of affine NA- Toda theories with one global U(1) symmetry. In particular we find the Lie algebraic condition defining a subclass of {\it T-selfdual} torsionless NA Toda models and their zero curvature representation.