  We present a systematic study of nonlinear and higher derivatives extensions
of electromagnetism. We clarify when action functionals S[F] can be explicitly
obtained from arbitrary (not necessarily self-dual) nonlinear equations of
motion. We show that the "Deformed twisted self-duality condition" proposal
originated in the context of supergravity counterterms is actually the general
framework needed to discuss self-dual theories starting from a variational
principle.
  We generalize to nonlinear and higher derivatives theories Schroedinger
formulation of Born-Infeld theory, and for the latter, and more in general for
nonlinear theories, we derive a closed form expression of the corresponding
deformed twisted self-duality conditions. This implies that the hypergeometric
expression entering these duality conditions and leading to Born-Infeld theory
satisfies a hidden quartic equation.
