  Generalized composite fluxbrane solutions for a wide class of intersection
rules are obtained. The solutions are defined on a manifold which contains a
product of n Ricci-flat spaces M_1 x ... x M_n with 1-dimensional M_1. They are
defined up to a set of functions H_s obeying non-linear differential equations
equivalent to Toda-type equations with certain boundary conditions imposed. A
conjecture on polynomial structure of governing functions H_s for intersections
related to semisimple Lie algebras is suggested. This conjecture is valid for
Lie algebras: A_m, C_{m+1}, m > 0. For simple Lie algebras the powers of
polynomials coincide with the components of the dual Weyl vector in the basis
of simple roots. Explicit formulas for A_1 + ... + A_1 (orthogonal),
"block-ortogonal" and A_2 solutions are obtained. Certain examples of solutions
in D = 11 and D =10 (II A) supergravities (e.g. with A_2 intersection rules)
and Kaluza-Klein dyonic A_2 flux tube, are considered.
