  Assuming that the space-time is close to isotropic in the sense that the
shear parameter is small and that the maximal velocity of the particles is
bounded, we have been able to show that for non-diagonal Bianchi I-symmetric
spacetimes with collisionless matter the asymptotic behaviour at late times is
close to the special case of dust. We also have been able to show that all the
Kasner exponents converge to 1/3 and an asymptotic expression for the induced
metric has been obtained. The key was a bootstrap argument.
