  A recently proposed nonlinear transport equation is used to model bulk
viscous cosmologies that may be far from equilibrium, as happens during viscous
fluid inflation or during reheating. The asymptotic stability of the de Sitter
and Friedmann solutions is investigated. The former is stable for bulk
viscosity index $q<1$ and the latter for $q>1$. New solutions are obtained in
the weakly nonlinear regime for $q=1$. These solutions are singular and some of
them represent a late-time inflationary era.
