Superconformal tensor calculus greatly simplifies the derivation of the component form of the lagrangian and supersymmetry transformation laws for supergravity-matter systems generally, if the extraneous gauge freedoms are fixed by a “natural” set of gauge conditions. We show this explicitly for the Yang-Mills matter supergravity system recently discussed by Cremmer et al. The present technique would be useful for the further study of a more general matter-supergravity system.