  In order to establish whether the unstable r-modes in a rotating neutron star
provide a detectable source of gravitational waves, we need to understand the
details of the many dissipative processes that tend to counteract the
instability. It has been established that the bulk viscosity due to exotic
particles, like hyperons, may be particularly important in this respect.
However, the effects of hyperon superfluidity have so far not been fully
accounted for. While the associated suppression of the reaction rates that give
rise to the bulk viscosity has been estimated, superfluid aspects of the fluid
dynamics have not been considered. In this paper we determine the r-mode
instability window for a neutron star with a $\Sigma^{-}$ hyperon core, using
the appropriate multifluid formalism including, for the first time, the effect
of the "superfluid" bulk viscosity coefficients. We demonstrate that, even
though the extra terms may increase the bulk viscosity damping somewhat, their
presence does not affect the qualitative features of the r-mode instability
window.
