We present a manifestly Lorentz invariant, space-time supersymmetric, and 'kappa-invariant' world-volume action for all type II Dirichlet p-branes, p less than or equal to 9, in a general type II supergravity background, including massive backgrounds in the IIA case. The p = 0, 2 cases are rederived from D = 11. The p = 9 case provides a supersymmetrization of the D = 10 Bom-Infeld action. (C) 1997 Elsevier Science B.V.