  The coset Sp(2,R)/U(1) is parametrized by two real scalar fields. We
generalize the formalism of auxiliary tensor (bispinor) fields in U(1)
self-dual nonlinear models of abelian gauge fields to the case of Sp(2,R)
self-duality. In this new formulation, Sp(2,R) duality of the nonlinear
scalar-gauge equations of motion is equivalent to an Sp(2,R) invariance of the
auxiliary interaction. We derive this result in two different ways, aiming at
its further application to supersymmetric theories. We also consider an
extension to interactions with higher derivatives.
