  We analyze characteristic properties of two different cosmological models:
(i) a one-component dark energy model where the bulk viscosity $\zeta$ is
associated with the fluid as a whole, and (ii) a two-component model where
$\zeta$ is associated with a dark matter component $\rho_{\rm m}$ only, the
dark energy component considered inviscid. Shear viscosity is omitted. We
assume throughout the simple equation of state $p=w\rho$, with $w$ a constant.
In the one-component model we consider two possibilities, either to take
$\zeta$ 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 $\alpha=1+w$ and the magnitude of $\zeta$. Second,
we consider the case $\zeta=~$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 $\zeta_{\rm m}$ is proportional to the square of
$\rho_{\rm m}$, 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 $\zeta_0\sim
10^6~$Pa s for the present viscosity is reasonable, and that the two-component
model seems to be favored.
