  We investigate perturbations of a class of spherically symmetric solutions in
massive gravity and bi-gravity. The background equations of motion for the
particular class of solutions we are interested in reduce to a set of the
Einstein equations with a cosmological constant. Thus, the solutions in this
class include all the spherically symmetric solutions in general relativity,
such as the Friedmann-Lema\^{i}tre-Robertson-Walker solution and the
Schwarzschild (-de Sitter) solution, though the one-parameter family of two
parameters of the theory admits such a class of solutions. We find that the
equations of motion for the perturbations of this class of solutions also
reduce to the perturbed Einstein equations at first and second order.
Therefore, the stability of the solutions coincides with that of the
corresponding solutions in general relativity. In particular, these solutions
do not suffer from non-linear instabilities which often appear in the other
cosmological solutions in massive gravity and bi-gravity.
