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We find one-loop correction to the integral kernel of the BFKL equation for the total cross section of the high energy scattering in QCD and calculate the next-to-leading contribution to anomalous dimensions of twist-2 operators near j = 1.The BFKL equation is very important for the theory of the Regge processes at high energies √ s in the perturbative QCD [1]. In particular, it can be used together with the DGLAP evolution equation [2] for the description of structure functions for the deep inelastic ep scattering at small values of the Bjorken variable x = −q 2 /(2pq), where p and q are the momenta of the proton and the virtul photon correspondingly. But up to recent years the integral kernel for the BFKL equation was known only in the leading logarithmic approximation (LLA), which did not allow one to find its region of applicapability, including the scale in transverse momenta fixing the argument of the QCD coupling constant α(ck 2 ⊥ ) and the longitudinal scale √ s 0 for the minimal initial energy. In this paper we calculate the QCD radiative corrections to this kernel.In LLA the gluon is reggeized and the Pomeron is a compound state of two reggeized gluons. One can neglect multi-gluon components of the Pomeron wave function also in the next-to-leading logarithmic approximation (NLLA) and express the total cross-section σ(s) for the high energy scattering of colourless particles A, B in terms of their impact factors Φ i ( − → q i ) and the t-channel partial wave G ω ( − → q , − → q ′ ) for the reggeized gluon scattering at t = 0:Here − → q and − → q ′ are transverse momenta of gluons with the virtualities − − → q 2 ≡ −q 2 and − − → q ′ 2 ≡ −q ′2 correspondingly, s = 2p A p B is the squared invariant mass of the colliding particles with momenta p A and p B . Note, that the dependence of the Regge factor from 1

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