  In this paper we study the future global existence and late-time behaviour of
the Einstein-Boltzmann system with Bianchi I symmetry and a positive
cosmological constant $\Lambda>0$. For the Boltzmann equation we consider the
scattering kernel of Israel particles which are the relativistic counterpart of
Maxwellian particles. Under a smallness assumption on initial data in a
suitable norm we show that solutions exist globally in time and isotropize at
late times.
