Fluctuations produced by the cosmological constant in the empty Bianchi type-IX model

We analyze the fluctuations of the gravitational field, produced by the cosmological term, in the empty Bianchi type-IX cosmological model. It is shown that such fluctuations do not change the process of alternation of Kasner eras very near to the singularity, and that a positive cosmological constant leads to an asymptotic isotropization of the model.