Non-perturbative effects for the BFKL equation in QCD and in N=4 SUSY
The gluon reggeization and BFKL equation in the Higgs model and QCD are reviewed. The BFKL is non-Fredholm one, which allows to predict its eigenvalue for all coupling constants at N=4 SUSY in the limit of large anomalous dimensions. The Green function in QCD in the next-to-leading approximation depends on a phase parameter related with the physics in the confinement region. We consider two different models for this dynamics and find the Pomeron spectrum.