  The multiplets that occur in four dimensional rigidly supersymmetric theories
can be described either by chiral superfields in Minkowski superspace or
analytic superfields in harmonic superspace. The superconformal Ward identities
for Green's functions of gauge invariant operators of these types are derived.
It is shown that there are no chiral superconformal invariants. It is further
shown that the Green's functions of analytic operators are severely restricted
by the superconformal Ward when analyticity is taken into account.
