  We consider a gravitational model in dimension D with several forms, l scalar
fields and a Lambda-term. We study cosmological-type block-diagonal metrics
defined on a product of an 1-dimensional interval and n oriented Einstein
spaces. As an electromagnetic composite brane ansatz is adopted and certain
restrictions on the branes are imposed the conformally covariant Wheeler-DeWitt
(WDW) equation for the model is studied. Under certain restrictions, asymptotic
solutions to the WDW equation are found in the limit of the formation of the
billiard walls. These solutions reduce the problem to the so-called quantum
billiard in (n + l - 1)-dimensional hyperbolic space. Several examples of
quantum billiards in the model with electric and magnetic branes, e.g.
corresponding to hyperbolic Kac-Moody algebras, are considered. In the case n=2
we find a set of basis asymptotic solutions to the WDW equation and derive
asymptotic solutions for the metric in the classical case.
