  Mutidimensional cosmological models with $n\left( n\geq 2\right) $ Einstein
spaces $M_i\left( i=1,\ldots ,n\right) $ are investigated. The cosmological
constant and homogeneous minimally coupled scalar field as a matter sources are
considered. The scalar field has a potential of general form depending on the
scalar field as well as on the scale factors of $M_i$ . The general condition
of existence of the solutions with spontaneous compactification is obtained and
applied to physically important cases. Two particular kinds of solutions are
found. One of them has a wormhole-type continuation into the Euclidean region.
Another one represents the generalization of the de Sitter universe to the
multidimensional model under consideration.
