  The implications of N=1 superconformal symmetry for four dimensional quantum
field theories are studied. Superconformal covariant expressions for two and
three point functions of quasi-primary superfields of arbitrary spin are found
and connected with the operator product expansion. The general formulae are
specialised to cases involving a scalar superfield L, which contains global
symmetry currents, and the supercurrent, which contains the energy momentum
tensor, and the consequences of superconformal Ward identities analysed. The
three point function of L is shown to have unique completely antisymmetric or
symmetric forms. In the latter case the superspace version of the axial anomaly
equation is obtained. The three point function for the supercurrent is shown to
have two linearly independent forms. A linear combination of the associated
coefficients for the general expression is shown to be related to the scale of
the supercurrent two point function through Ward identities. The coefficients
are given for the two free field superconformal theories and are also connected
with the parameters present in the supercurrent anomaly for supergravity
backgrounds. Superconformal invariants, which are possible even in three point
functions, are discussed.
