  An analysis is presented of the Bianchi type I cosmological models with a
bulk viscosity when the universe is filled with the stiff fluid $p = \epsilon$
while the viscosity is a power function of the energy density, such as $\eta =
\alpha |\epsilon|^n$. Although the exact solutions are obtainable only when the
$2n$ is an integer, the characteristics of evolution can be clarified for the
models with arbitrary value of $n$. It is shown that, except for the $n = 0$
model that has solutions with infinite energy density at initial state, the
anisotropic solutions that evolve to positive Hubble functions in the later
stage will begin with Kasner-type curvature singularity and zero energy density
at finite past for the $n> 1$ models, and with finite Hubble functions and
finite negative energy density at infinite past for the $n < 1$ models. In the
course of evolution, matters are created and the anisotropies of the universe
are smoothed out. At the final stage, cosmologies are driven to infinite
expansion state, de Sitter space-time, or Friedman universe asymptotically.
However, the de Sitter space-time is the only attractor state for the $n <1/2 $
models. The solutions that are free of cosmological singularity for any finite
proper time are singled out. The extension to the higher-dimensional models is
also discussed.
