A complete proof of the quark Reggeization hypothesis in the leading
logarithmic approximation for any quark--gluon inelastic process in the
multi--Regge kinematics in all orders of αs is given. First, we show
that the multi--Regge form of QCD amplitudes is guarantied if a set of
conditions on the Reggeon vertices and the trajectories is fulfilled. Then, we
examine these conditions and show that they are satisfied.Comment: 22 pages, 7 figures, use elsart.cl