  We expand the generic model involving chiral matter, super Yang-Mills gauge
fields, and supergravity to second order in the gravity and gauge prepotentials
in a manifestly covariant and conformal way. Such a class of models includes
conventional chiral matter coupled to supergravity via a conformal compensator.
This is a first step toward calculating one-loop effects in supergravity in a
way that does not require a perturbative expansion in the inverse Planck scale
or a recourse to component level calculations to handle the coupling of the
K\"ahler potential to the gravity sector. We also consider a more restrictive
model involving a linear superfield in the role of the conformal compensator
and investigate the similarities it has to the dual chiral model.
