  The higher spin properties of the non-abelian bosonization in the classical
theory are investigated. Both the symmetry transformation algebra and the
classical current algebra for the non-abelian free fermionic model are linear
Gel'fand-Dickey type algebras. However, for the corresponding WZNW model these
algebras are different. There exist symmetry transformations which algebra
remains the linear Gel'fand-Dickey algebra while in the corresponding current
algebra nonlinear terms arised. Moreover, this algebra is closed (in Casimir
form) only in an extended current space in which nonlinear currents are
included. In the affine sector, it is necessary to be included higher isotopic
spin current too. As result we have a triple extended algebra.
