  We continue our investigation of the nonlinear SUSY for complex potentials
started in the Part I (math-ph/0610024) and prove the theorems characterizing
its structure in the case of non-diagonalizable Hamiltonians. This part
provides the mathematical basis of previous studies. The classes of potentials
invariant under SUSY transformations for non-diagonalizable Hamiltonians are
specified and the asymptotics of formal eigenfunctions and associated functions
are derived. Several results on the normalizability of associated functions at
infinities are rigorously proved. Finally the Index Theorem on relation between
Jordan structures of intertwined Hamiltonians depending of the behavior of
elements of canonical basis of supercharge kernel at infinity is proven.
