  We investigate the classical symmetries of the dynamics of the null-dust
spherically symmetric Vaidya spacetime. Einstein's equations for this model can
be obtained as equations of motion of a two-dimensional field theory. We
discuss the transformations leaving invariant such equations of motion. These
are given by two distinct sets, the residual diffeomorphisms coming from
general relativity and the generalisation of the Schr\"odinger symmetry,
recently found for the static Schwarzschild black holes. Surprisingly, these
two sets represent the symmetries of two different action functionals, leading
to the same equations of motion, but with different phase spaces.
