  High orders of perturbation theory can be calculated by the Lipatov method,
whereby they are determined by saddle-point configurations (instantons) of the
corresponding functional integrals. For most field theories, the Lipatov
asymptotics has the functional form c a^N \Gamma(N+b) (N is the order of
perturbation theory), and the relative corrections to it have a form of a
series in powers of 1/N. It is shown that this series diverges factorially and
its high-order coefficients can be calculated using a procedure similar to
Lipatov's one. The K-th expansion coefficient has the form
const(\ln(S1/S0))^{-K}\Gamma(K+(r1-r0)/2), where S0 and S1 are the values of
the action for the first and the second instanton of the field theory under
consideration, while r0 and r1 are the corresponding numbers of zero modes. The
instantons satisfy the same equation as in the Lipatov method and are assumed
to be renumbered in order of increasing of their action. This result has the
universal character and is valid in any field theory for which the Lipatov
asymptotic form is as specified above.
