  We consider spacetime metrics with a given (but quite generic) dependence on
a dimensionful parameter such that in the 0 and infinity limits of that
parameter the metric becomes singular. We study the isometry groups of the
original spacetime metrics and of the singular metrics that arise in the limits
and the corresponding symmetries of the motion of p-branes evolving in them,
showing how the Killing vectors and their Lie algebras can be found in general.
We illustrate our general results with several examples which include limits of
anti-de Sitter spacetime in which the holographic screen is one of the singular
metrics and of pp-waves.
