  We consider generic linear perturbations of a nonbidiagonal class of static
black-hole solutions in massive (bi)gravity. We show that the quasinormal
spectrum of these solutions coincides with that of a Schwarzschild black hole
in general relativity, thus proving that these solutions are mode stable. This
is in contrast to the case of bidiagonal black-hole solutions which are
affected by a radial instability. On the other hand, the full set of
perturbation equations is generically richer than that of a Schwarzschild black
hole in general relativity, and this affects the linear response of the black
hole to external perturbations. Finally, we argue that the generalization of
these solutions to the spinning case does not suffer from the superradiant
instability, despite the fact that the theory describes a massive graviton.
