The multiplets that occur in four dimensional rigidly supersymmetric theories can be described either by chiral super elds in Minkowski superspace or analytic super elds 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 which implies that chiral Green's functions are determined up to constants. It is further shown that analytic superconformal invariants are severely restricted such that when internal space analyticity is taken into account, the four point Green's functions are also determined up to constants. These results suggest that the superconformal Ward identities are su cient to determine all the Green's functions of these operators.