  In this paper we investigate the constant volume exponential solutions (i.e.
the solutions with the scale factors change exponentially over time so that the
comoving volume remains the same) in the Einstein-Gauss-Bonnet gravity. We find
conditions for these solutions to exist and show that they are compatible with
any perfect fluid with the equation of state parameter $\omega<1/3$ if the
matter density of the Universe exceeds some critical value. We write down some
exact solutions which generalize ones found in our previous paper for models
with a cosmological constant.
