Supersymmetric duality rotations

We derive Script N = 1,2 superfield equations as the conditions for a (nonlinear) theory of one abelian Script N = 1 or Script N = 2 vector multiplet to be duality invariant. The Script N = 1 super Born-Infeld action is a particular solution of the corresponding equation. A family of duality invariant nonlinear Script N = 1 supersymmetric theories is described. We present the solution of the Script N = 2 duality equation which reduces to the Script N = 1 Born-Infeld action when the (0,1/2) part of Script N = 2 vector multiplet is switched off. We also propose a constructive perturbative scheme to compute duality invariant Script N = 2 superconformal actions.