  Large order asymptotic behaviour of renormalization constants in the minimal
subtraction scheme for the $\phi ^4$ $(4-\epsilon)$ theory is discussed.
Well-known results of the asymptotic $4-\epsilon $ expansion of critical
indices are shown to be far from the large order asymptotic value. A {\em
convergent} series for the model $\phi ^4$ $(4-\epsilon)$ is then considered.
Radius of convergence of the series for Green functions and for renormalisation
group functions is studied. The results of the convergent expansion of critical
indices in the $4-\epsilon $ scheme are revalued using the knowledge of large
order asymptotics. Specific features of this procedure are discussed.
