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We construct the general four-dimensional N=2 supergravity theory coupled tovector and vector-tensor multiplets only. Consistency of the constructionrequires the introduction of the vector fields dual to those sitting in thesame supermultiplets as the antisymmetric tensors, as well as the scalar fieldsdual to the tensors themselves. Gauge symmetries also involving theseadditional fields guarantee the correct counting of the physical degrees offreedom.

D=4, N=2 Gauged Supergravity coupled to Vector-Tensor Multiplets