- We present a systematic study of a new type of consistent "brane-world Kaluza-Klein reduction," which describes fully nonlinear deformations of codimension one objects that arise as solutions of a large class of gauged supergravity theories in diverse dimensions, and whose world-volume theories are described by ungauged supergravities with-one half of the original supersymmetry. In addition, we provide oxidations of these anstz which are in general related to sphere compactified higher dimensional string theory or M-theory. Within each class we also provide explicit solutions of brane configurations localized on the world-brane. We show that at the Cauchy horizon (in the transverse dimension of the consistently Kaluza-Klein reduced world-brane) there is a curvature singularity for any configuration with a non-null Riemann curvature or a nonvanishing Ricci scalar that lives in the world-brane. Since the massive Kaluza-Klein modes can be consistently decoupled, they cannot participate in regulating these singularities. 2001 American Institute of Physics.