  We report the results of a study on the dynamical compactification of
spatially flat cosmological models in Einstein-Gauss-Bonnet gravity. The
analysis was performed in the arbitrary dimension in order to be more general.
We consider both vacuum and $\Lambda$-term cases. Our results suggest that for
vacuum case, realistic compactification into the Kasner (power law) regime
occurs with any number of dimensions ($D$), while the compactification into the
exponential solution occurs only for $D \geqslant 2$. For the $\Lambda$-term
case only compactification into the exponential solution exists, and it only
occurs for $D \geqslant 2$ as well. Our results, combined with the bounds on
Gauss-Bonnet coupling and the $\Lambda$-term ($\alpha, \Lambda$, respectively)
from other considerations, allow for the tightening of the existing constraints
and forbid $\alpha < 0$.
