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We investigate exponential solutions (i.e. the solutions with the scale factors change ex- potentially over time so that the comoving volume remains the same) in the Einstein-Gauss- Bonnet gravity. We obtain all possible exact vacuum and Λ-term cosmological solution in (4+1) and (5+1) dimensions, generalize some of these solutions to the arbitrary number of spatial dimensions and obtain necessary conditions for exponential solutions to exist in the presence of matter in the form of perfect fluid.