Effective world-brane actions for solitons of ten-dimensional type IIA
and IIB superstring theory are derived using the formulation of solit
ons as Dirichlet branes. The one-brane actions are used to recover pre
dictions of SL(2, Z) strong-weak coupling duality. The two-brane actio
n, which contains a hidden eleventh target-space coordinate, is shown
to be the eleven-dimensional supermembrane action. It can be thought o
f as the membrane action of ''M-theory''.