  The self-duality of the N=1 supersymmetric Born--Infeld action implies a
double self-duality of the tensor multiplet square-root action when the scalar
and the antisymmetric tensor are interchanged via Poincare' duality. We show
how this phenomenon extends to D space-time dimensions for non-linear actions
involving pairs of forms of rank p and D-p-2. As a byproduct, we construct a
new two-field generalization of the Born-Infeld action whose equations of
motion are invariant under a U(1) duality. In these systems, the introduction
of Green-Schwarz terms results in explicit non-linear mass-like terms for dual
massive pairs.
