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A general two-dimensional fractional supersymmetric conformal field theory isinvestigated. 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 thecomponent-fields of supermultiplets are calculated. Then the logarithmicsuperconformal field theories are investigated and the chiral and fulltwo-point functions are obtained.Comment: 13 pages, Latex, no figure

Two-dimensional fractional supersymmetric conformal and logarithmic conformal field theories and two point functions