  We derive the DGLAP and BFKL evolution equations in the N=4 supersymmetric
gauge theory in the next-to-leading approximation. The eigenvalue of the BFKL
kernel in this model turns out to be an analytic function of the conformal spin
|n|. Its analytic continuation to negative |n| in the leading logarithmic
approximation allows us to obtain residues of anomalous dimensions \gamma of
twist-2 operators in the non-physical points j=0,-1,... from the BFKL equation
in an agreement with their direct calculation from the DGLAP equation.
Moreover, in the multi-color limit of the N=4 model the BFKL and DGLAP dynamics
in the leading logarithmic approximation is integrable for an arbitrary number
of particles. In the next-to-leading approximation the holomorphic separability
of the Pomeron hamiltonian is violated, but the corresponding Bethe-Salpeter
kernel has the property of a hermitian separability. The main singularities of
anomalous dimensions \gamma at j=-r obtained from the BFKL and DGLAP equations
in the next-to-leading approximation coincide but our accuracy is not enough to
verify an agreement for residues of subleading poles.
