of $y$. It will be valid for all the Bianchi models since we will see that these 3 quantities keep the same forms each time the same set of equilibrium points is considered.\
From (\[v2\]) and the asymptotical forms for $\Omega(t)$, we deduce that the potential behaves as $t^{-2}$ when $\ell$ tends toward a non vanishing constant, or as a non vanishing constant otherwise (the same behaviour held when we consider the Bianchi type $I$ model[@Fay01]). Concerning the 3-curvature which can be expressed as $R^{(3)}=e^{2\Omega+4(\beta_++\sqrt{3}\beta_-)}$, it is obvious that near isotropy, it tends to zero, showing that the Universe becomes spatially flat.\
Let us note the importance of the potential for isotropisation of the Bianchi type $II$ model. If we consider $U=0$, we get from the field equations (\[ppp\]) and (\[hamp\]) that $H=p_++p_0$ and thus $\dot{\beta}_+=1-p_0H^{-1}$, $p_0$ being an integration constant. It follows that $\dot{\beta}_+$ does not asymptotically vanish and isotropy can not be reached.\
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*Partial equilibrium[^3]*\
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Above we have defined the isotropic equilibrium states such that all the variables reach equilibrium. However, this last statement is not mandatory: all of them have not to reach equilibrium such that $x_\pm\rightarrow 0$ in a stable way. In this case, 