  We investigate analytic properties of the six point planar amplitude in N=4
SUSY at the multi-Regge kinematics for final state particles. For inelastic
processes the Steinmann relations play an important role because they give a
possibility to fix the phase structure of the Regge pole and Mandelstam cut
contributions. These contributions have the Moebius invariant form in the
transverse momentum subspace. The analyticity and factorization constraints
allow us to reproduce the two-loop correction to the 6-point BDS amplitude in
N=4 SUSY obtained earlier in the leading logarithmic approximation with the use
of the s-channel unitarity. The exponentiation hypothesis for the remainder
function in the multi-Regge kinematics is also investigated. The 6-point
amplitude in LLA can be completely reproduced from the BDS ansatz with the use
of the analyticity and Regge factorization.
