[en] A general construction of affine nonabelian (NA)-Toda models in terms of the axial and vector gauged two loop WZNW model is discussed. They represent integrable perturbations of the conformal σ-models (with tachyons included) describing (charged) black hole type string backgrounds. We study the off-critical T-duality between certain families of axial and vector type 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 T-selfdual torsionless NA-Toda models and their zero curvature representation