  The multi--Regge form of QCD amplitudes with gluon exchanges is proved in the
next-to-leading approximation. The proof is based on the bootstrap relations,
which are required for the compatibility of this form with the s-channel
unitarity. We show that the fulfillment of all these relations ensures the
Reggeized form of energy dependent radiative corrections order by order in
perturbation theory. Then we prove that all these relations are fulfilled if
several bootstrap conditions on the Reggeon vertices and trajectory hold true.
Now all these conditions are checked and proved to be satisfied.
