  The truncated Israel-Stewart theory of irreversible thermodynamics is used to
describe the bulk viscous pressure and the anisotropic stress in a class of
spatially homogeneous viscous fluid cosmological models. The governing system
of differential equations is written in terms of dimensionless variables and a
set of dimensionless equations of state is utilized to complete the system. The
resulting dynamical system is then analyzed using standard geometric
techniques. It is found that the presence of anisotropic stress plays a
dominant role in the evolution of the anisotropic models. In particular, in the
case of the Bianchi type I models it is found that anisotropic stress leads to
models that violate the weak energy condition and to the creation of a periodic
orbit in some instances. The stability of the isotropic singular points is
analyzed in the case with zero heat conduction; it is found that there are
ranges of parameter values such that there exists an attracting isotropic
Friedmann-Robertson-Walker model. In the case of zero anisotropic stress but
with non-zero heat conduction the stability of the singular points is found to
be the same as in the corresponding case with zero heat conduction; hence the
presence of heat conduction does not apparently affect the global dynamics of
the model.
