For the description of the Universe expansion, compatible with observational data, a model of Lovelock gravity
with dilaton is investigated. D-dimensional space with 3- and (D-4)-dimensional maximally symmetric subspaces is
considered. Space without matter and space with perfect fluid are under test. In various forms of the theory (third order
without dilaton and second order with dilaton and without it) there are obtained stationary, power-law, exponential and
exponent-of-exponent form cosmological solutions. Last two forms include solutions which are clear to describe
accelerating expansion of 3-dimensional subspace. Also there is a set of solutions describing cosmological expansion
which does not tend to isotropization in the presence of matter.