Behaviour of effective charges in finite theories in curved space-time

Behaviour of effective charges in one - loop finite theories in curved space - time is investigated. It is shown that in strong gravitational field the effective charge corresponding to the papameter of non - minimal interaction between scalar and gravitational fields tends to its conformal value or else increases exponentially. The one - loop potential in finite theories is obtained with the accuracy up to terms linear in curvature. It is shown that in the presence of the external supergravity the supersymmetric finite theories admit of asymptotical conformal invariance