SO(4)-invariant extended supergravity

We present results on an extended supergravity theory which has an internal SO(4) symmetry. All terms in the Lagrangian and transformation rules are determined through order ${\kappa }^2$, and some ${\kappa }^3$ terms in $\mathcal{L}$ are given. A complicated feature of this theory, not present in previous extended supergravity models, is a strongly indicated nonpolynomial structure in the scalar fields. This theory contains as a special case SO(2) extended supergravity coupled to its Abelian vector multiplet.