Abstract
In this paper we employ the construction of the Dirac bracket for the remaining current of 
deformed Kac - Moody algebra when constraints similar to those connecting the sl(2)-Wess - Zumino - Witten model and the Liouville theory are imposed to show that it satisfies the q-Virasoro algebra proposed by Frenkel and Reshetikhin. The crucial assumption considered in our calculation is the existence of a classical Poisson bracket algebra induced in a consistent manner by the correspondence principle, mapping the quantum generators into commuting objects of classical nature preserving their algebra.