We comment on the off-critical perturbations of WZNW models by a mass
term as well as by another descendent operator, when we can compare th
e results with further algebra obtained from the Dirac quantization of
the model, in such a way that a more general class of models be inclu
ded. We discover, in both cases, hidden Kac-Moody algebras obeyed by s
ome currents in the off-critical case, which in several cases are enou
gh to completely fix the correlation functions.