Rapidly rotating neutron stars can be unstable with respect to emission of gravitational waves. In this case so-called r-mode oscillations develop. Bulk viscosity is one of the principal mechanisms suppressing oscillations of the neutron-star matter. It arises from non-equilibrium reactions of mutual transformations of particles. We calculate the bulk viscosity of superfluid hyperonic matter. For this purpose, the dissipati e relativistic hydrodynamics, which describes superfluid mixtures, has been generalized to the case where both nucleons and hyperons are superfluid. We show that in the most general case (with superfluid neutrons, protons, Λ and Σ^- hyperons) non-equilibrium processes give rise to 16 coefficients of bulk viscosity, of which only 4 are independent. Incidentally an error in the expression of the bulk viscosity of normal (non-superfluid) matter, widely rooted in the literature, is corrected.

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