before the decoupling between matter and radiation, we have no indication about Universe’s geometry. Was it as so symmetric as the FLRW models imply? Thus, it seems interesting to generalise them by only keeping their spatial homogeneity property. Bianchi models describe anisotropic cosmological models and may allow to understand the process leading to an isotropic Universe. The most studied Bianchi models are those containing the FLRW solutions[@ColHaw73], i.e. the types $I$, $V$, $VII_{0,h}$ and $IX$. We have examined the Bianchi type $I$ model in [@Fay01]. Here, we will be interested in the Bianchi class $A$ models with curvature.

Our goal is to look for necessary conditions allowing the isotropisation of Bianchi class $A$ models with curvature when a minimally coupled and massive scalar tensor theory is considered. We will then deduce the common asymptotical behaviour of the metric functions when isotropisation is reached and compare our results with those obtained for the Bianchi type $I$ model[@Fay01]. From a technical point of view, we will use the methods of [@Fay01]: we will get the field equations from ADM Hamiltonian formalism[@Nar72; @MatRyaTot73] and rewrite them with a new set of variables. Then we will look for equilibrium points corresponding to isotropic stable 