  The higher spin symmetry for both Dirac and Majorana massless free fermionic
field models are considered. An infinite Lie algebra which is a linear
realization of the higher spin extension of the cross products of the Virasoro
and affine Kac-Moody algebras is obtained. The corresponding current algebra is
closed which is not the case of annalogous current algebra in the WZNW model.
The gauging procedure for the higher spin symmetry is given also.
