We study the asymptotic behaviour of the Bianchi type VI _ { 0 } 
universes with a tilted \gamma -law perfect fluid .
The late-time attractors are found for the full 7-dimensional state space and for several interesting invariant subspaces .
In particular , it is found that for the particular value of the equation of state parameter , \gamma = 6 / 5 , there exists a bifurcation line which signals a transition of stability between a non-tilted equilibrium point to an extremely tilted equilibrium point .
The initial singular regime is also discussed and we argue that the initial behaviour is chaotic for \gamma < 2 .