  We consider numerically dynamics of a flat anisotropic Universe in
Einstein-Gauss-Bonnet gravity with positive $\Lambda$ in dimensionalities 5+1
and 6+1. We identify three possible outcomes of the evolution, one singular and
two nonsingular. First nonsingular outcome is oscillatory. Second is the known
exponential solution. The simplest version of it is the isotropic de Sitter
solution. In Gauss-Bonnet cosmology there exist also anisotropic exponential
solutions. When an exponential solution being an outcome of cosmological
evolution has two different Hubble parameters, the evolution leads from
initially totally anisotropic stage to a sum of two isotropic subspaces. We
show that such type of evolution is rather typical and possible even in the
case when de Sitter solution also exists.
