  Supersymmetry can be consistently generalized in one and two dimensional
spaces, fractional supersymmetry being one of the possible extension. 2D
fractional supersymmetry of arbitrary order $F$ is explicitly constructed using
an adapted superspace formalism. This symmetry connects the fractional spin
states ($0,{1 \over F}, ...,{F-1 \over F}$). Besides the stress momentum
tensor, we obtain a conserved current of spin($1 + {1 \over F})$. The coherence
of the theory imposes strong constraints upon the commutation relations of the
modes of the fields. The creation and annihilation operators turn out to
generate alternative statistics, currently referred as quons in the literature.
We consider, with a special attention, the consistence of the algebra, on the
level of the Hilbert space and the Green functions. The central charges are
generally irrational numbers except for the particular cases $F=2,3,4$. A
natural classification emerges according to the decomposition of $F$ into its
product of prime numbers leading to sub-systems with smaller symmetries.
