  We discuss DGLAP and BFKL evolution equations in the N=4 supersymmetric gauge
theory in the leading and next-to-leading approximations. Eigenvalues of the
BFKL kernel in this model turn out to be analytic functions of the conformal
spin. It allows us to find the residues of the anomalous dimensions of the
twist-2 operators in the points j=1,0,-1, ... from the BFKL equation in an
agreement with their direct calculation from the DGLAP equation. The
holomorphic separability of the BFKL kernel and the integrability of the DGLAP
dynamics in this model are also discussed.
