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Nonlinear self-duality in N = 2 supergravity

For nonlinear models of an Abelian vector supermultiplet coupled to N = 2 supergravity in four dimensions, we formulate the self-duality equation which expresses invariance under U(1) duality rotations. In the flat space limit, this equation reduces to the N = 2 self-duality equation proposed in hep-th/0001068. We also give an example of a self-dual locally supersymmetric model containing a higher-derivative extension of the Born-Infeld action at the component level.