  A general two-dimensional fractional supersymmetric conformal field theory is
investigated. The structure of the symmetries of the theory is studied.
Applying the generators of the closed subalgebra generated by
$(L_{-1},L_{0},G_{-1/(F+1)})$ and
$(\bar{L}_{-1},\bar{L}_{0},\bar{G}_{-1/(F+1)})$, the two point functions of the
component-fields of supermultiplets are calculated. Then the logarithmic
superconformal field theories are investigated and the chiral and full
two-point functions are obtained.
