Summary: "Generalized p-brane black-hole solutions for a wide class of intersection rules are presented. The solutions are defined on a manifold that contains a product of n-1 Ricci-flat `internal' spaces. They are determined up to functions H_s=H_s(R) obeying nonlinear differential equations (equivalent to Toda-type equations) with boundary conditions of special type. Using a conjecture on a polynomial structure of H_s for intersections related to Lie algebras, new A_2-dyon solutions are obtained. Two examples of A_2-dyon solutions, i.e., a dyon in D=11 supergravity with M2- and M5-branes intersecting at a point and a dyon in Kaluza-Klein theory, are considered."