  NON-ABELIAN TODA THEORIES are shown to provide EXACTLY SOLVABLE conformal
systems in the presence of a BLACK HOLE which may be regarded as describing a
string propagating in target space with a black-hole metric. These theories are
associated with non-canonical $\bf Z$-gradations of simple algebras, where the
gradation-zero subgroup is non-abelian. They correspond to gauged WZNW models
where the gauge group is nilpotent and are thus basically different from the
ones currently considered following Witten. The non-abelian Toda potential
gives a cosmological term which may be exactly integrated at the classical
level.
