The quantum integrability of a class of massive perturbations of the p
arafermionic conformal field theories associated to compact Lie groups
is established by showing that they have quantum conserved densities
of scale dimension 2 and 3. These theories are integrable for any valu
e of a continuous vector coupling constant, and they generalize the pe
rturbation of the minimal parafermionic models by their first thermal
operator. The classical equations of motion of these perturbed theorie
s are the non-abelian affine Toda equations which admit (charged) soli
ton solutions whose semi-classical quantization is expected to permit
the identification of the exact S-matrix of the theory. (C) 1997 Elsev
ier Science B.V.