  Multidimensional cosmological model describing the evolution of n+1 Einstein
spaces in the theory with several scalar fields and forms is considered. When a
(electro-magnetic composite) p-brane Ansatz is adopted the field equations are
reduced to the equations for Toda-like system. The Wheeler-De Witt equation is
obtained. In the case when n "internal" spaces are Ricci-flat, one space M_0
has a non-zero curvature, and all p-branes do not "live" in M_0, the classical
and quantum solutions are obtained if certain orthogonality relations on
parameters are imposed. Spherically-symmetric solutions with intersecting
non-extremal p-branes are singled out. A non-orthogonal generalization of
intersection rules corresponding to (open, closed) Toda lattices is obtained. A
chain of bosonic D > 11 models (that may be related to hypothetical higher
dimensional supergravities and F-theories) is suggested.
