  We consider thick domain walls in a de Sitter universe following paper by
Basu and Vilenkin. However, we are interested not only in stationary solutions
found therein, but also investigate the general case of domain wall evolution
with time. When the wall thickness parameter, $\delta_0$, is smaller than
$H^{-1}/\sqrt{2}$, where $H$ is the Hubble parameter in de Sitter space-time,
then the stationary solutions exist, and initial field configurations tend with
time to the stationary ones. However, there are no stationary solutions for
$\delta_0 \geq H^{-1}/\sqrt{2}$. We have calculated numerically the rate of the
wall expansion in this case and have found that the width of the wall grows
exponentially fast for $\delta_0 \gg H^{-1}$. An explanation for the critical
value $\delta_{0c} = H^{-1}/\sqrt{2}$ is also proposed.
