  We perform the OPE analysis of the contribution of colour-singlet compound
states of reggeized gluons to a generic hard process in QCD and calculate the
spectrum of the corresponding higher twist anomalous dimensions in multi-colour
limit. These states govern high energy asymptotics of the structure functions
and their energies define the intercept of the Regge singularities both in the
Pomeron and the Odderon sectors. We argue that due to nontrivial analytical
properties of the energy spectrum, the twist expansion does not hold for the
gluonic states with the minimal energy generating the leading Regge
singularities. It is restored however after one takes into account the states
with larger energies whose contribution to the Regge asymptotics is subleading.
