  A 2D- fractional supersymmetry theory is algebraically constructed. The
Lagrangian is derived using an adapted superspace including, in addition to a
scalar field, two fields with spins 1/3,2/3. This theory turns out to be a
rational conformal field theory. The symmetry of this model goes beyond the
super Virasoro algebra and connects these third-integer spin states. Besides
the stress-momentum tensor, we obtain a supercurrent of spin 4/3. Cubic
relations are involved in order to close the algebra; the basic algebra is no
longer a Lie or a super-Lie algebra. The central charge of this model is found
to be 5/3. Finally, we analyse the form that a local invariant action should
take.
