We compute the bulk viscosity of a mixed quark-hadron phase. In the first scenario to be discussed, the mixed phase occurs at large densities and we assume that it is composed of a mixing of hyperonic matter and quarks in the Color Flavor Locked phase. In a second scenario, the mixed phase occurs at lower densities and it is composed of a mixing of nucleons and unpaired quark matter. We have also investigated the effect of a non-vanishing surface tension at the interface between hadronic and quark matter. In both scenarios, the bulk viscosity is large when the surface tension is absent, while the value of the viscosity reduces in the second scenario when a finite value for the surface tension is taken into account. In all cases, the r-mode instabilities of the corresponding hybrid star are suppressed.

8 pages, 7 figures, extended version in print on Phys.Rev.D