  We discuss in some detail the properties of a novel class of Weyl-conformally
invariant p-brane theories which describe intrinsically light-like branes for
any odd world-volume dimension and whose dynamics significantly differs from
that of the ordinary (conformally non-invariant) Nambu-Goto p-branes. We
present explicit solutions of the WILL-brane (Weyl-Invariant Light-Like brane)
equations of motion in various gravitational backgrounds of physical relevance
exhibiting the following new phenomena: (i) In spherically symmetric static
backgrounds the WILL-brane automatically positions itself on (materializes) the
event horizon of the corresponding black hole solutions, thus providing an
explicit dynamical realization of the membrane paradigm in black hole physics;
(ii) In product spaces (of interest in Kaluza-Klein context) the WILL-brane
wrappes non-trivially around the compact (internal) dimensions and moves as a
whole with the speed of light in the non-compact (space-time) dimensions.
