  In certain string inspired higher dimensional cosmological models it has been
conjectured that there is generic, chaotic oscillating behavior near the
initial singularity -- the Kasner parameters which characterize the asymptotic
form of the metric "jump" between different, locally constant values and
exhibit a never-ending oscillation as one approaches the singularity. In this
paper we investigate a class of cosmological solutions with form fields and
diagonal metrics which have a "maximal" number of composite electric S-branes.
We look at two explicit examples in D=4 and D=5 dimensions that do not have
chaotic oscillating behavior near the singularity. When the composite branes
are replaced by non-composite branes chaotic oscillating
