A recently proposed nonlinear transport equation is used to model bulk
viscous cosmologies that may be far from equilibrium, as happens duri
ng viscous fluid inflation or during reheating. The asymptotic stabili
ty of the de Sitter and Friedmann solutions is investigated. The forme
r is stable for bulk viscosity index q < 1 and the latter for q > 1. N
ew solutions are obtained in the weakly nonlinear regime for q = 1. Th
ese solutions are singular and some of them represent a late-time infl
ationary era.