  The large-order behaviour of QCD is dominated by renormalons. On the other
hand renormalons do not occur in conformal theories, such as the one describing
the infrared fixed-point of QCD at small beta_0 (the Banks--Zaks limit). Since
the fixed-point has a perturbative realization, all-order perturbative
relations exist between the conformal coefficients, which are renormalon-free,
and the standard perturbative coefficients, which contain renormalons.
Therefore, an explicit cancellation of renormalons should occur in these
relations. The absence of renormalons in the conformal limit can thus be seen
as a constraint on the structure of the QCD perturbative expansion. We show
that the conformal constraint is non-trivial: a generic model for the
large-order behaviour violates it. We also analyse a specific example, based on
a renormalon-type integral over the two-loop running-coupling, where the
required cancellation does occur.
