  We extend the notion of central charge superspace to the case of local
supersymmetry. Gauged central charge transformations are identified as
diffeomorphisms at the same footing as space-time diffeomorphisms and local
supersymmetry transformations. Given the general structure we then proceed to
the description of a particular vector-tensor supergravity multiplet of 24+24
components, identified by means of rather radical constraints.
