  Non-Abelian fractional supersymmetry algebra in two dimensions is introduced
utilizing $U_q(sl(2,\Rcc))$ at roots of unity. Its representations and the
matrix elements are obtained. The dual of it is constructed and the
corepresentations are studied. Moreover, a differential realization of the
non-Abelian fractional supersymmetry generators is given in the generalized
superspace defined by two commuting and two generalized Grassmann variables. An
invariant action under the fractional supersymmetry transformations is given.
