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We study $D$-dimensional Einstein-Gauss-Bonnet gravitational model includingthe Gauss-Bonnet term and the cosmological term $\Lambda$. We find a class ofsolutions with exponential time dependence of two scale factors, governed bytwo Hubble-like parameters $H >0$ and $h$, corresponding to factor spaces ofdimensions $m >2$ and $l > 2$, respectively. These solutions contain afine-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 apolynomial equation of either fourth or third order and may be solved inradicals. The explicit solution for $m = l$ is presented in Appendix. Imposingcertain restrictions on $x$, we prove the stability of the solutions in a classof cosmological solutions with diagonal metrics. We also consider a subclass ofsolutions with small enough variation of the effective gravitational constant$G$ and show the stability of all solutions from this subclass.

Stable exponential cosmological solutions with two factor spaces in the Einstein-Gauss-Bonnet model with a $\Lambda$-term