section will be parsed into three subsections. The first one will be devoted to the Bianchi type $II$ model, the second one to the Bianchi types $VI_0$ and $VII_0$ and the third one to the Bianchi type $VIII$ and $IX$ models. Each of these subsections will be divided into two subsections devoted to the field equations and the study of the equilibrium points. We will discuss the physical meaning of our results in section \[s3\].

Mathematical study of isotropisation for class $A$ Bianchi models {#s1}
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We begin calculating the Hamiltonian field equations. The Lagrangian of the minimally coupled scalar-tensor theory is given by: $$\label{action1}
S=(16\pi)^{-1}\int \left[R-(3/2+\omega(\phi))\phi^{,\mu}\phi_{,\mu}\phi^{-2} -U(\phi)\right]\sqrt{-g}d^4 x$$ Although it may be more natural to redefine $\phi$ so that the kinetic term takes a standard form $\phi^{,\mu}\phi_{,\mu}$, we prefer considering an unspecified Brans-Dicke coupling function such that our results be valid for any form of $\omega(\phi)$ even when it is analytically impossible to get $\phi(\omega)$. The general form of the metric for Bianchi models is written: $$\label{metrique}
ds^2 = -(N^2 -N_i N^i )d\Omega^2 + 2N_i d\Omega\omega^i + R_0 ^2 g_{ij}\omega^i \omega^j$$ The $\omega_i$ are the 1-forms defining each Bianchi model. $N$ and $N^i$ are respectively the lapse and shift 