  We study $D$-dimensional Einstein-Gauss-Bonnet gravitational model including
the Gauss-Bonnet term and the cosmological term $\Lambda$. We find a class of
solutions with exponential time dependence of two scale factors, governed by
two Hubble-like parameters $H >0$ and $h$, corresponding to factor spaces of
dimensions $m >2$ and $l > 2$, respectively. These solutions contain a
fine-tuned $\Lambda = \Lambda (x, m, l, \alpha)$, which depends upon the ratio
$h/H = x$, dimensions of factor spaces $m$ and $l$, and the ratio $\alpha =
\alpha_2/\alpha_1$ of two constants ($\alpha_2$ and $\alpha_1$) of the model.
The master equation $\Lambda(x, m, l,\alpha) = \Lambda$ is equivalent to a
polynomial equation of either fourth or third order and may be solved in
radicals. The explicit solution for $m = l$ is presented in Appendix. Imposing
certain restrictions on $x$, we prove the stability of the solutions in a class
of cosmological solutions with diagonal metrics. We also consider a subclass of
solutions with small enough variation of the effective gravitational constant
$G$ and show the stability of all solutions from this subclass.
