The SL(2,R) duality symmetric action for the Born-Infeld theory in ter
ms of two potentials, coupled with nontrivial background fields in fou
r dimensions, is established. This construction is carried out in deta
il by analyzing the Hamiltonian structure of the Born-Infeld theory. T
he equivalence with the usual Born-Infeld theory is shown. [S0556-2821
(98)01114-X].