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We show that massless solutions to the Einstein-Vlasov system in a Bianchi Ispace-time with small anisotropy, i.e. small shear and small trace-free part ofthe spatial energy momentum tensor, tend to a radiation fluid in an Einstein-deSitter space-time with the anisotropy $\Sigma^a_b\Sigma^b_a$ and $\tilde{w}^i_j\tilde{w}^j_i$ decaying as $O(t^{-\frac12})$.

On the future of solutions to the massless Einstein-Vlasov system in a Bianchi I cosmology