A general construction of affine nonabelian (NA)-Toda models in terms of th
e axial and vector gauged two loop WZNW model is discussed. They represent
integrable perturbations of the conformal sigma -models (with tachyons incl
uded) describing (charged) black hole type string backgrounds. We study the
off-critical T-duality between certain families of axial and vector type i
ntegrable 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 s
ubclass of T-selfdual torsionless NA-Toda models and their zero curvature r
epresentation. (C) 2001 Academic Press.