  We present a comprehensive analysis of classical scalar, vector and tensor
cosmological perturbations in ghost-free massive bigravity. In particular, we
find the full evolution equations and analytical solutions in a wide range of
regimes. We show that there are viable cosmological backgrounds but, as has
been found in the literature, these models generally have exponential
instabilities in linear perturbation theory. However, it is possible to find
stable scalar cosmological perturbations for a very particular choice of
parameters. For this stable subclass of models we find that vector and tensor
perturbations have growing solutions. We argue that special initial conditions
are needed for tensor modes in order to have a viable model.
