is not compatible with isotropy. The above reasoning concerning the case for which $1-\ell^2\rightarrow 0$ faster than $\Omega^{-1}$ will stay valid for any Bianchi model. However, when $1-\ell^2\rightarrow 0$ slower than $\Omega^{-1}$, it will be valid only for Bianchi type $II$, $VI_0$ and $VIII$ models. For Bianchi type $VII_0$ and $IX$ models, the situation is different because when $\beta_\pm\rightarrow 0$ during isotropisation, $p_\pm$ varies slower than $e^{-2\Omega}$ since $\partial V/\partial \beta_\pm e^{4\Omega}\rightarrow 0$. However, we will show below that near equilibrium, the value $\ell=1$ can also be excluded.\
Now it is possible to show that $p_\pm e^{3\Omega}$ vanishes when $\Omega\rightarrow -\infty$. Writing $\dot{p}_\pm/H$ as a function of $x_\pm$ and $w$ and using their asymptotical behaviours, we calculate that $\dot{p}_\pm/p_\pm$ tends toward the constant $-(1+\ell^2)$. Consequently $p_\pm e^{3\Omega}\rightarrow e^{(2-\ell^2)\Omega}\rightarrow 0$ when $\Omega\rightarrow -\infty$ and the necessary but not sufficient condition for isotropisation is respected. Moreover, from (\[hamp1\]), we calculate that asymptotically $\dot{H}H^{-1}$ tends toward $\ell^2-3$. Thus $H\rightarrow e^{(\ell^2-3)\Omega}$ and diverges since $\ell^2<1$: therefore, although determined independently, the asymptotical behaviours of $p_\pm$ and $H$ agreed with these of $x_\pm=p_\pm H^{-1}$.

Concerning the scalar field, we can find a differential equation whose solution asymptotically behaves in the same way as $\phi$ when $\Omega\rightarrow 