We analyze characteristic properties of two different cosmological models: (i) a one-component dark energy model where the bulk viscosity ζ is associated with the fluid as a whole, and (ii) a two-component model where ζ is associated with a dark matter component ρm only, the dark energy component considered inviscid. Shear viscosity is omitted. We assume throughout the simple equation of state p = wρ, with w a constant. In the one-component model we consider two possibilities, either to take ζ proportional to the scalar expansion (equivalent to the Hubble parameter), in which case the evolution becomes critically dependent on the value of the small constant α = 1 + w and the magnitude of ζ. Second, we consider the case ζ = const., where a de Sitter final stage is reached in the future. In the two-component model we consider only the case where the dark matter viscosity ζm is proportional to the square of ρm, where again a de Sitter form is found in the future. In this latter case the formalism is supplemented by a phase space analysis. As a general result of our considerations we suggest that a value ζ0 ∼ 10 6 Pa s for the present viscosity is reasonable, and that the two-component model seems to be favored. 95.36.+x