  The dynamics of solutions of the Einstein-Vlasov system with Bianchi I
symmetry is discussed in the case of massive or massless particles. It is shown
that in the case of massive particles the solutions are asymptotic to isotropic
dust solutions at late times. The initial singularity is more difficult to
analyse. It is shown that the asymptotic behaviour there must be one of a small
set of possibilities but it is not clear whether all of these possibilities are
realized. One solution is exhibited in the case of massless particles which
behaves quite differently near the singularity from any Bianchi I solution with
perfect fluid as matter model. In particular the matter is not dynamically
negligeable near the singularity for this solution.
