  We investigate diagonal Bianchi-I spacetimes in the presence of viscous
fluids by using the shear and the anisotropic pressure components as the basic
variables, where the viscosity is driven by the (second-order) causal
thermodynamics. A few exact solutions are presented, among which we mention the
anisotropic versions of de Sitter/anti-de Sitter geometries as well as an
asymptotically isotropic spacetime presenting an effective constant cosmic
acceleration without any cosmological constant. The qualitative analysis of the
solutions for barotropic fluids with linear equations of state suggests that
the behaviour is quite general.
