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The coset Sp(2,R)/U(1) is parametrized by two real scalar fields. Wegeneralize 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 nonlinearscalar-gauge equations of motion is equivalent to an Sp(2,R) invariance of theauxiliary interaction. We derive this result in two different ways, aiming atits further application to supersymmetric theories. We also consider anextension to interactions with higher derivatives.

Auxiliary tensor fields for Sp(2,R) self-duality