We formulate world-volume actions that describe the dynamics of Dirich
let p-branes in a flat 10d background. The fields in these theories co
nsist of the 10d superspace coordinates (X(m), theta) and an abelian w
orld-volume gauge held A(mu). The global symmetries are given by the N
= 2A or N = 2B super-Poincare group, according to whether p is even o
r odd. The local symmetries in the (p + I)-dimensional world volume ar
e general coordinate invariance and a fermionic kappa symmetry.