  We describe a large class of solutions in pure gravity, dilaton gravity and
supergravity corresponding to extended higher-dimensional black holes with
strong (non-linear) gravitational waves propagating along their worldvolume.
For pure gravity, the extended black holes are higher-dimensional analogs of
the point-like Schwarzschild black hole in four dimensions. For supergravity,
they are non-extremal p-branes. The gravitational waves can be both
space-filling and localized around the worldvolume of the extended black holes.
The solutions we present contain a large number of arbitrary functions of the
light-cone time describing the amplitudes of different non-linear gravitational
wave modes.
