  We show that the SL(2,R) duality symmetry of type IIB superstring theory can
be formulated as the canonical transformation interchanging momenta and
magnetic degrees of freedom associated to the abelian world-volume gauge field
of the D-3-brane. D-strings are shown to be connected under the corresponding
transformation in the world-sheet to the (m,n) family of string solutions of
type IIB supergravity constructed by Schwarz. For the type IIA superstring the
D-2-brane is mapped under the three dimensional world-volume electric-magnetic
duality to the dimensional reduction of the membrane of M-theory.
