  The massive soliton theories describe integrable perturbations of WZW cosets
as generalized multi-component sine-Gordon models. We study their coupling to
2-dim gravity in the conformal gauge and show that the resulting models can be
interpreted as conformal non-Abelian Toda theories when a certain algebraic
condition is satisfied. These models, however, do not provide quantum
mechanically consistent string backgrounds in the case the underlying WZW
constraints are first solved classically.
