  We look for necessary isotropisation conditions of Bianchi class $A$ models
with curvature in presence of a massive and minimally coupled scalar field when
a function $\ell$ of the scalar field tends to a constant, diverges
monotonically or with sufficiently small oscillations. Isotropisation leads the
metric functions to tend to a power or exponential law of the proper time $t$
and the potential respectively to vanish as $t^{-2}$ or to a constant.
Moreover, isotropisation always requires late time accelerated expansion and
flatness of the Universe.
