  We study the stability under the perturbation and the related
anti-evaporation of the Nariai space-time in bigravity. If we impose specific
condition for the solutions and parameters, we obtain asymptotically de Sitter
space-time, and show the existence of the Nariai space-time as a background
solution. Considering the perturbation around the Nariai space-time up to first
order, we investigate the behavior of black hole horizon. We show that the
anti-evaporation does not occur on the classical level in the bigravity.
