Supersymmetric duality rotations

We derive N = 1, 2 superfield equations as the conditions for a (nonlinear) theory of one abelian N = 1 or N = 2 vector multiplet to be duality invari ant. The N = 1 super Born-Infeld action is a particular solution of the cor responding equation. A family of duality invariant nonlinear N = 1 supersym metric theories is described. We present the solution of the N = 2 duality equation which reduces to the N = 1 Born-Infeld action when the (0, 1/2) pa rt of N = 2 vector multiplet is switched off. We also propose a constructiv e perturbative scheme to compute duality invariant N = 2 superconformal act ions.