  We study next-to-leading corrections to the integral kernel of the BFKL
equation for high energy cross-sections in QCD and in supersymmetric gauge
theories. The eigenvalue of the BFKL kernel is calculated in an analytic form
as a function of the anomalous dimension \gamma of the local gauge-invariant
operators and their conformal spin n. For the case of an extended N=4 SUSY the
kernel is significantly simplified. In particular, the terms non-analytic in n
are canceled. We discuss the relation between the DGLAP and BFKL equations in
the N=4 model.
