  The nature of cosmological solutions for a homogeneous, anisotropic Universe
given by a Bianchi type-I (BI) model in the presence of a Cosmological constant
$\Lambda$ is investigated by taking into account dissipative process due to
viscosity. The system in question is thoroughly studied both analytically and
numerically. It is shown the viscosity, as well as the $\Lambda$ term exhibit
essential influence on the character of the solutions. In particular a negative
$\Lambda$ gives rise to an ever-expanding Universe, whereas, a suitable choice
of initial conditions plus a positive $\Lambda$ can result in a
singularity-free oscillatory mode of expansion. For some special cases it is
possible to obtain oscillations in the exponential mode of expansion of the BI
model even with a negative $\Lambda$, where oscillations arise by virtue of
viscosity.
