  We consider the dynamics of a causal bulk viscous cosmological fluid filled
constantly decelerating Bianchi type I space-time. The matter component of the
Universe is assumed to satisfy a linear barotropic equation of state and the
state equation of the small temperature Boltzmann gas. The resulting
cosmological models satisfy the condition of smallness of the viscous stress.
The time evolution of the relaxation time, temperature, bulk viscosity
coefficient and comoving entropy of the dissipative fluid is also obtained.
