Supersymmetric duality rotations

We deriveN =1;2supereld equations astheconditions fora (nonlin- ear) theory of one abelianN =1orN=2 vector multiplet to be duality invariant. The N = 1 super Born-Infeld action is a particular solution of the corresponding equation. A family of duality invariant nonlinearN =1 supersymmetric theories is described. We present the solution of theN = 2 duality equation which reduces to theN = 1 Born-Infeld action when the (0;1=2) part ofN = 2 vector multiplet is switchedo. Wealsoproposeaconstructiveperturbativeschemetocomputeduality invariantN =2 superconformal actions.