  We find an infinite set of new noncommuting conserved charges in a specific
class of perturbed CFT's and present a criterion for their existence.They
appear to be higher momenta of the already known commuting conserved
currents.The algebra they close consists of two noncommuting$W_\infty$
algebras.We find various Virasoro subalgebras of the full symmetry algebra. It
is shown on the examples of the perturbed Ising and Potts models that one of
them plays an essencial role in the computation of the correlation functions of
the fields of the theory.
