We study the lattice analogues of the Wess-Zumino-Witten (WZW) and Tod
a conformal field theories. We describe discrete versions of the Drinf
el'd-Sokolov reduction and the Sugawara construction for the WZW model
, and show how to formulate a perturbation theory in the chiral sector
, We describe the spaces of integrals of motion of the perturbed theor
ies. We interpret the perturbed WZW model in terms of NLS hierarchy an
d obtain an embedding of this model into the lattice KP hierarchy.