We discuss BFKL equations for composite states of Reggeized gluons in the color singlet and adjoint representations in the next-to-leading logarithmic approximation (NLLA). In an accordance with the non-Fredholm properties of the corresponding kernels, their eigenvalues in N = 4 SUSY are calculated for arbitrary couplings at large values of anomalous dimensions. The Green function for the BFKL equation in LLA with the running coupling in QCD is expressed in terms of non-perturbative phases of eigenfunctions. It allows to construct the spectrum of Pomerons for two different models of the QCD dynamics at large distances.
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