  A (n+1)-dimensional cosmological model with a set of scalar fields and
antisymmetric (p+2)-form is considered. Some of scalar fields may have negative
kinetic terms, i.e. they may describe ``phantom'' fields. For certain odd
dimensions (D = 4m+1 = 5, 9, 13, ...) and (p+2)-forms (p = 2m-1 = 1, 3, 5, ...)
and non-exceptional dilatonic coupling vector $\vec{\lambda}$ we obtain
cosmological-type solutions to the field equations. These solutions are
characterized by self-dual or anti-self-dual charge density forms Q (of rank
2m) and may describe the maximal set of branes (i.e. when all the branes have
non-zero charge densities). Some properties of these solutions are considered,
e.g. Kasner-like behavior, the existence of non-singular (e.g. bouncing)
solutions and those with acceleration. The solutions with bouncing and
acceleration take place when at least there is one ``phantom'' field in the
model.
