  We discuss properties of a new class of p-brane models, describing
intrinsically lightlike branes for any world-volume dimension, in various
gravitational backgrounds of interest in the context of black hole physics. One
of the characteristic features of these lightlike p-branes is that the brane
tension appears as an additional nontrivial dynamical world-volume degree of
freedom. Codimension one lightlike brane dynamics requires that bulk space with
a bulk metric of spherically symmetric type must possess an event horizon which
is automatically occupied by the lightlike brane while its tension evolves
exponentially with time. The latter phenomenon is an analog of the well known
"mass inflation" effect in black holes.
