  For the SL(2,\textbf{R}) duality-invariant generalization of Maxwell
electrodynamics in the presence of both electric and magnetic sources, we
formulate a local, manifestly duality-symmetric, Zwanziger-type action by
introducing a pair of four-potentials $A^\mu$ and $B^\mu$ in a judicious way.
On the two potentials $A^\mu$ and $B^\mu$ the SL(2,\textbf{R}) duality
transformation acts in a simple linear manner. In quantum theory including
charged source fields, this action can be recast as a
SL(2,\textbf{Z})-invariant action. Also given is a Zwanziger-type action for
SL(2,\textbf{R}) duality-invariant Born-Infeld electrodynamics which can be
important for D-brane dynamics in string theory.
