  The vacuum cosmological model on the manifold $R \times M_1 \times \ldots
\times M_n$ describing the evolution of $n$ Einstein spaces of non-zero
curvatures is considered. For $n = 2$ the Einstein equations are reduced to the
Abel (ordinary differential) equation and solved, when $(N_1 = $dim $ M_1, N_2
= $ dim$ M_2) = (6,3), (5,5), (8,2)$. The Kasner-like behaviour of the
solutions near the singularity $t_s \to +0$ is considered ($t_s$ is synchronous
time). The exceptional ("Milne-type") solutions are obtained for arbitrary $n$.
For $n=2$ these solutions are attractors for other ones, when $t_s \to +
\infty$. For dim $ M = 10, 11$ and $3 \leq n \leq 5$ certain two-parametric
families of solutions are obtained from $n=2$ ones using "curvature-splitting"
trick. In the case $n=2$, $(N_1, N_2)= (6,3)$ a family of non-singular
solutions with the topology $R^7 \times M_2$ is found.
