  Composite fluxbrane and S-brane solutions for a wide class of intersection
rules are considered. These solutions are defined on a product manifold R_{*} x
M_1 x ... x M_n which contains n Ricci-flat spaces M_1, ..., M_n with
1-dimensional factor spaces R_{*} and M_1. They are determined up to a set of
functions obeying non-linear differential equations equivalent to Toda-type
equations with certain boundary conditions imposed. Exact solutions
corresponding to configurations with two branes and intersections related to
simple Lie algebras C_2 and G_2 are obtained. In these cases, the functions
H_s(z), s =1,2, are polynomials of degrees (3, 4) and (6, 10), respectively, in
agreement with a conjecture put forward previously in Ref., \cite{Iflux}. The
S-brane solutions under consideration, for special choices of the parameters,
may describe an accelerating expansion of our 3-dimensional space and a small
enough variation of the effective gravitational constant.
